Maths-
General
Easy
Question
A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?
Hint:
Find the edge length of the cube and then find the area of one face of the tank.
The correct answer is: 25 ft^2
Complete step by step solution:
Volume of the cube shaped fish tank = 125 cubic feet…(i)
Let the side of fish tank = x
We know that the formula for volume of a cube =
…(ii)
On equating both, we get ![x cubed equals 125](data:image/png;base64,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)
Now take cube roots on both the sides, we have ![x equals cube root of 125](data:image/png;base64,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)
![not stretchy rightwards double arrow x equals 5 ft](data:image/png;base64,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)
We know that a cube is a three dimensional shape made of 6 equal squares.
Hence area of one cube face = x2
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow x squared equals 5 squared end cell row cell not stretchy rightwards double arrow 25 ft squared end cell end table](data:image/png;base64,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)
Hence area of one cube face of fish tank = 25 ft2
Related Questions to study
Maths-
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
![](data:image/png;base64,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)
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
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)
Maths-General
Maths-
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
Maths-General
Maths-
Solve the equation m2 = 14
Solve the equation m2 = 14
Maths-General
Maths-
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
Maths-General
Maths-
Maths-General
Maths-
The angles of a triangle are
Find the value of and then the angles of the triangle
The angles of a triangle are
Find the value of and then the angles of the triangle
Maths-General
Maths-
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
Maths-General
Maths-
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Maths-General
Maths-
Maths-General
Maths-
In
, DA = DB = DC. Show that
.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAB/CAYAAACHZaLpAAAVdElEQVR4nO3deVxU9d4H8M/MsIqyywyCIZipFzRNbhg9mqbxqIldFYvFVyLd0pDCAJFNRDYFBZkAL64XTROX8nELJTLimqU9KZqKiGKoJIuyODAMMHO+zx/tT6IwMBwGfu8/gfmdz7z8+Dv7OQIiIjAMj4R8B2AYVkKGd6yEDO9YCRnesRIyvGMlZHjHSsjwjpWQ4R0rIcM7VkKmU9rqqlBTUQGFqvvGZCVkOqXs66PYuvUgbj3svrO9rIRMh3HNVTh95jh2HMjHuWvl3TYuKyHTQUr8eOMS6vXHwWVULXb/zyncae6e2ZCVkOkQlbwK174+g6Hu87Dk1ecgO5eH07dqwXXD2KyETAcoUX/3O3x5eyicJENg5zwZw5qv4tihb1HZ2vXRdbo+BNPXUdt9fPfJIXyeX47iq8ehL2zBjz/VofVkHopfn4ohIwZ0aXxWQuaJ6ksu4nv5RMT/KwJ/s9SHkCM03ziNyLidOP55ESaPcIVuF8Znq2PmMQjyyu9wICsNX13/X9QKjGBnNwzDhllC0NwAvcar+GLPBmQXFONhFzYO2UzIPIYAIr3BcJr5FgY1EWwGCsERICLAQDwCnmGpaCEBJJb6EHVlKeweE6Y9Dx48wL3Kajxl9xSMBxppbDlsdcw80s2bNxEbG4u5/5iDA/tyNLostjpm/uL8+fOIi4tDfn4+Ghsbcf36dY0uj82EzG9aWlpw/PhxrFy5EufPn8eCBQtgZGQETW+xsZmQAQA0NjZi//79SEpKgqmpKdLT0/HUU0/hyJEjrISM5lVVVWHbtm3Yvn07Ro4ciZUrV2LKlCm4du2axgsIsBL2e7dv30ZiYiIOHTqEF154AatXr8b48eMBoEcKCLAS9lscx+Hs2bNISUlBYWEhXn/9dYSEhMDOzq7Hs7AS9kNKpRL5+fkICwvDvXv3EBwcjEWLFkEikfCSh5Wwn5HL5dizZw8yMzNBRFi7di28vLxgaGjIWyZWwn6koaEBGzZswKZNm+Do6IjY2Fi89NJLEAgEvOZiJewnSktLsX79ehw8eBBTp05FbGwsHB0d+Y4FgJWwz+M4DufOncO6detQVFSEZcuWITAwEJaWlnxH+w0rYR/W1taG3NxcJCYmorq6GiEhIfDz88OAAV27CLW7sRL2UXK5HDk5OUhISIChoSHWrFmDBQsWwMDAgO9of8FK2AdVVFQgIyMD+/fvh0Qi+W0HREend/5z985UjNpKSkqwceNGHDx4EG5ubggNDcWYMWMgEnXlslPNYiXsI4gI3377LRISElBUVITFixfD398f9vb2fEd7IlbCPuDXHZA1a9bg/v37CAoKgq+vL8zNzfmO1iGshFru4cOHyM7OxqZNm2BiYoLU1FTMmjWL1zMgncVKqMUqKiqwefNmZGVlwdXVFeHh4XBxceE7VqexEmqp4uJiJCcnIy8vD7NmzUJ4eDhGjhzJdyy1sBJqGZVKhaKiIoSEhOD777/H0qVLERISAisrK76jqY2VUIsoFAocOXIEycnJkMlkiIiIwDvvvKM1OyDtYSXUEg0NDdi9ezekUilEIhHWrl2LWbNm9cozIJ3FSqgFqqurkZqaii1btsDZ2RmxsbGYOHEi37G6DSthL0ZEKCkpwYYNG/Dpp5/C3d0dwcHBGDt2LN/RuhUrYS/FcRwKCgqQmJiIsrIyBAUF4e2334ZYLOY7WrdjJeyFWlpacOLECcTFxaGxsRGrVq2Ct7c39PX1+Y6mEayEvczDhw+xbds2fPjhh5BIJEhKSsLs2bN79QUIXcVK2IuUl5dj69at2Lp1K5599llERUXB1dW1TxcQYCXsNa5du4bo6GgUFBRg5syZfXIHpD2shDxTKpUoLCxEUlISrly5Al9fX3zwwQewtrbmO1qPYSXkWU5ODtavXw+ZTIbo6Gh4e3tj4MCBfMfqUayEPKmqqsK+ffsglUphYWGBuLg4uLm59YkzIJ3FSsiDO3fuQCqVIicnBy+88AJWrlyJCRMm8H4TOl9YCXvYxYsXsW7dOpw6dQpeXl4IDQ3FkCFD+I7FK1bCdhGULQq0KDkIIADHqUAAINSBoYEBdESdn7UKCwsRHR2NkpISLF26FAEBARg8eHC3J9c2rITtUbWhJDcDmz45gx9lIgwebAkDkRJNdboYO2UmFix8BU8NMuzQ85YbGxtx+PBhpKamora2FjExMfDy8oKxsbHGv4Y2YM+sbo9ID8+8+BpchxjifosR5iwLR2RkKN50H4nvtq/CB3GbUVrT8sRh6urqsHnzZgQHB0MkEiElJQW+vr6sgH/AZsLH0LWwgY14MEzNdWE/wg5DjYChC4fCWlSP5Ws/xb/HvIK4hY7QbWfNXFFRgbS0NOzcuRMTJkzAqlWr4Orq2rNfQguwmfBxiIOK40AcB5Xy1x8a4pmX3fGsWA/nThehsu3RH/3hhx8QEBCA3bt3w8PDA1KplBWwHWwmVINo0EDYGnO4+NMdyFUq4A8v1eI4DidPnkRaWhouXLgAf39/vPvuu33yEqzuwkqoBlWjDLcbBOCGD8UA0e8rE5lMhmPHjiE+Ph66urpIT0+Hh4dHn78AoatYCR9HIIRIKIRAKMRvPSIZrpw8giv1gMuk8ZDo/bxBWFtbiy1btiAjIwMjR45EREQEpk2bxl92LcJK+Bgt1eUo/6kKdfd1UXq1FMbmLSj5Jh97tuZjuKc/3p49Err4eQckMTERn3zyCVxcXBAZGQlnZ2e+42sNVsL2qFpRdi4X39e0QWJEOPnvNHwlUELeZoLnliTCc/6LsNYX4NzZs5B++CEKCwsxb948hISEwN7evt+eglMHK2F7RLp42m0pEl5eAiEAFacCESAU6cHIyBDEqZD/eT6iV6/GrbIyhIeH4+2334aRkeZeydpXsRK2SwBdAyPoPuI38qYm5Ozbh/T0dJSUlMDQ0BDV1dVQKBSshGpgJeyk+vp6ZGVlIT09HcOGDcPGjRtRUFCA7Oxs1NXVITAwEKNGjeI7plZhJeyEGzduIDk5Gbm5uZg8eTJCQ0Mxbtw4eHh4ICMjAzt27MCtW7cQExOD559/HkIhOxfQIcR0yIULF2ju3LlkbGxMK1asoJqamj/9Xi6Xk1QqJTMzM3JxcaG8vDyeknafq1evkrm5OYWEhGh0Oey/6hMolUrk5ubi/fffx4ULFxATE4OIiIi/vAfE0NAQfn5+SE9PR0tLC9577z1s3rwZbW3tnNdjfqfRimu5xsZG2rVrFw0dOpQcHR1p+/btJJfLH/sZlUpF+fn55OrqSjY2NrR+/fq/zJraoqdmQlbCdtTU1NDq1avJ1taWnJyc6Pjx48RxXIc+y3EcXbp0iRYsWEAGBgb0z3/+k65fv67hxN2vp0rIdkweobS0FFKpFAcOHMCkSZMQHR2N0aNHd/gAtEAgwJgxY7BhwwbY29sjJycHlZWVCA0N7Rc3s3eaRiuuZTiOo7Nnz9Ls2bNJLBZTUFAQ3bx5s0tj1tbWUkpKCtnb25OTkxMdOXKEWlpauimxZrEdkx6mUCiQn5+P5cuXo6ioCIGBgQgPD4eDg0OXxjUzM4O/vz+Sk5Ohp6eHyMhIZGVloa6urpuSaz+2OsbPl2B99NFHyMzMhKGhIVJSUuDu7t5tr2EwMDCAh4cHHBwcEBcXh3Xr1qG6uhrLli3rV09aaJdG51ktUFlZSbGxsWRra0vu7u709ddfa3R5xcXFtHDhQpJIJLRkyRIqKSnR6PK6gu2Y9ICSkhKkpqbiyJEjmDZtGsLCwuDk5KTRZY4aNQrx8fEYMmQIdu3ahVu3biEhIaF/X/ql0Yr3Ukqlks6dO0evvfYamZub0wcffEBlZWU9mqG2tpaSkpJo+PDhNHnyZDp69CgpFIoezfAk7DihhrS1tdHhw4fJycmJRowYQQkJCXT//n1esjQ3N9OhQ4fIycmJbG1tKT09nR4+fMhLlkdhq2MNkMlk+Pjjj5GamgoAiImJwfz583l7DK+BgQHc3d1hYWGBhIQExMfH4/bt23j//fdha2vLSyZeaLTivUhVVRVFRUWRra0tTZ8+nb788ktqbW3lO9ZvLl++TL6+vmRubk6+vr5UUlJCSqWS10xsddyNbt68SX5+fiQSicjT05OuXLnCd6RHqq2tpdjYWBKLxeTi4kJfffUVr3lYCbsBx3H0n//8h2bMmEG2trYUFRVFlZWVfMd6rObmZsrOzqZnnnmGnJ2daf/+/bydYWHbhF2kUChw4sQJJCcno7a2FqtXr4aPj0+vfw+wgYEBfHx8MGjQICQmJmLVqlWoqamBt7c3TE1N+Y6nEX3ytF1zczO2bduGwMBAKBQKxMfHw9fXt9cX8Fc6OjqYO3cuNm7cCAcHB0RERCAlJQUymYzvaBrR52bC27dvY9euXcjKysLw4cOxevVqTJ48GTo62vVVBQIBJk2aBDMzM6xduxY7d+7EvXv3EBgYCCcnp751S6lGV/Y97PLly+Tt7U2Wlpb05ptv0vnz5/mO1C0qKyspPDycJBIJTZ8+nb744ose2XNmOyadoFQqqbCwkGbPnk12dna0fPlyKi8v5ztWt6qvr6esrCxydHSkcePG0Z49ezR+hoXtmHSQSqXCoUOHkJiYiLq6OgQFBWHx4sUYNGgQ39G6lYmJCXx9fWFlZYW4uDiEhYWhtrYWb7zxhtY/clirS1hXV4c9e/YgMzMT+vr6SElJgZubW599D4i+vj7c3d3h4OCAxMRErFu3DqWlpQgNDYWNjQ3f8dSn0XlWg3766ScKCwsjsVhM8+bN6zPbfx119+5deu+998jKykpjB+DZ6vgxLl26hLS0NBw7dgzz5s1DaGhol6+A1jY2NjYIDw+HsbExtm/fjoaGBgQFBWH69Ol8R+s8jVZcA7755ht66aWXyMLCgiIiInr9GRBNq6+vp+zsbLK1tSVHR0fKzc3ttrHZPSb/j1wux969e+Hv74+ysjKsWbMG4eHh/f4xvCYmJli4cCGkUinMzMzg5+f321kibaEVq+P6+nrs2rULqampsLCwwIYNG/Dqq6+yJ2D9QiQSYe7cubC2tkZ8fDwyMjJQXV0Nf39/7dhM0eg82w0qKiooJCSELC0taebMmXTmzBm+I/Vq5eXl9O6775KxsTHNmTOHLl26pPZY7GA1EZWWlpKnpyeZm5vTokWLqLi4mO9IWqGyspLWrFlDEomEXn75ZcrLy1PrSpx+vU2oUqlw8uRJBAQE4MyZMwgICMDatWvZc/86SCwWIywsDFKpFPX19QgMDMTevXvR1NTEd7RH6nXbhM3NzTh8+DCSk5OhVCqRkJCABQsW8HYJvrbS09ODh4cHrKysEBUVhZiYGDx48AB+fn697pKwXjUTNjQ0YMuWLQgPD4eBgQGSkpLg4+PDCqgmoVCIKVOmICkpCU5OTkhJSUF0dDSqqqr4jvZnGl3Zd8KdO3coMDCQBg8eTHPmzKHTp0+TSqXiO1afwHEc3bhxg5YsWUIWFha0aNEiunz58hOfMtavdkyKiorIx8eHrK2tydPTk4qLizv8GDam4+7cuUMJCQlkbW1NkyZNory8PGpra2v37/tFCVtbW+nUqVM0ZcoUsrKyoujoaKqoqOAzUp/X2tpKWVlZNHbsWBo9ejTt2LGDZDLZI/+2z587bm5uxoEDB5CamgqFQoG4uDh4enqy9wBrmK6uLt566y3Y2dkhLi4OUVFRuHv3LgICAmBmZsZPKI1WvB0NDQ2UmppKEomEnJ2d6dixY73qHuD+QKVS0eXLl2n+/PkkkUho6dKlf3k4U6+eCYlTok2pAiAAEf3yUyFEujrQET7+3oeysjJs3LgRx44dw6RJk7BixQo4Ozv3rXsmtIBQKISjoyMyMzMhlUqxZ88e3Lt3D5GRkZgwYUKPvv5CrRLWXMzFjt0HcaVGAAOjAdAXEhSterBz9cQ73i4Q6z/6CxQVFSEpKQkFBQXw9vZGcHAwhgwZ0qUvwHSNWCxGeHg4TE1NkZaWhhUrViAyMhKvvPJKO0UkNDc2oKGxGUJdQ5iYmUCXAyAEhE+YgNojiomJiensh/QHGEF55woOF5bAZdFy+Ex/HrbcHezcdgCVZiMw0ckGen+MTYT8/HyEhYXhwoULCAkJQXBw8F9ew8DwQ19fH+PHj8fQoUNx4sQJHD58GBYWFjA3N8dHH32E8ePHw83NDVAqUHXxM0gzpdi04xMUXChCjUqOy0VNMDUxh7npo17C9mRqzYQ6JkPg4DAc4sF38czYsXC0N4Lj6MEo//Er7Pvua9z7x9/x9C/Hl5uamvDZZ59h1apVEIlEiI2NhZeXF7sCppcZMGAAPD09YWFhgbi4OMTHx8PZ2RlyuRyCX2bEG99sQVJ8LmznvIcPAyfCsOUW8o9uRlbxGIz8+xgMV3PZau4dEziOg0rZhsaHTWhp04GsvAzXivUxbOpwmPxSQJlMhszMTGRkZEChUMDHxweWlpYoKCj4w7Yk01sIBAKoVCrMmDEDn376Kfbt2welUgmRSAiS38TeTUdQO2YxYt+cBetBAGAOr0XL0Hr4JgRoBmCg1nLVPkQjFOmg4eYP2BKxDHlmItQ3KaArdkfYqxNh/uvgOjq4ePEiKioqIBaLkZ+fj5MnT4LjOHUXy2iYQCCASCSCXC6Hrq4uxGIJxjiOhuzHr3C05AFenDsGkj/cyKhn8je8MdMGGDhA7WWqXUJOpcRA26fx6rKVePXpgWh6cBVH/7UNH25SIDhyOZ6zEMLAwACLFy+Gi4sLhEIhVCqV2kGZniUUCkFEsLUdipn/PQ2Ka1tRL1JCz5DDn3Y/BLowturatr2aJRRAAEBvgDHsRo3GSAcjAA5ounQWR9O+x4WFD/CcxWAIBAJMmzYNU6dO7VJIhj9CoQgiEdAmNIVJmwiyeg4E/LmIxIEgUPswm3rHCVsaUd9QB1mjDA+qqlFrZgx51fc49fmXwIgXMcz8920DkUjE3mDUBwy0/S94PLMFBfkFuO42FiPFP1dHpahC8ReXMMBpHBzs1LsJX0Bq7CHUFB3H1q07UHBDAathDrAcIERrQyUaRWaYtXQl/jFuGAxE7OBz38LhzjcfY23EbggnTIfbjIkw1VOg6cdbaCE7/H3OFNiY6T15mEdQq4TK5oeokzWBIyE4lQo/DyCAntEgmJoM7H1XyjLdggioLsrH0RMncaPREDoCEexHvYAZs1/GEFMdqDvtqFVCpr8jcNwvU49QqHb5fsVKyPCuV13ez/RPrIQM71gJGd4JT58+jeTkZJSVlT3xj59++mkIBJ0/KJmTk/On8f39/SEQCHD69OlOB2b6HmF8fDxWrlzZoT/Ozs5WayFeXl5qfY7pH/4PURGsn427jxwAAAAASUVORK5CYII=)
In
, DA = DB = DC. Show that
.
![](data:image/png;base64,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)
Maths-General
Maths-
In the figure, if
and
find x and y.
![](data:image/png;base64,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)
In the figure, if
and
find x and y.
![](data:image/png;base64,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)
Maths-General
Maths-
Would you classify the number 200 as a perfect square , a perfect cube , both or neither ?
Would you classify the number 200 as a perfect square , a perfect cube , both or neither ?
Maths-General
Maths-
Maths-General
Maths-
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C . Prove that
![A E squared plus B D squared equals A B squared plus D E squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAARCAYAAACmTIw3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAsBJREFUeNrtmDFIHEEUhgcRCwlCCpHjCEIQuSrYiFhdE4KIhHAg4QhHCEIKsbAQUqYIaVIdIgEREQsJWKQQSRMsJEiacBwpBZGUaSyCxXEI5xt8B8sw83Z25u3OrdkHf+HuOPu/b9/MvR0h0oseqgs6A02J/ERevRfMHWMItApqifxFXr0XzB2jI/IbncL3/fdeBZ3mFFZevf83zNctqr2nURe3bRkl7DEeZ7DybkB/QBegI3w25fcadAiaNMyZlfekzOPyzJJ5Ep7s9fIS/3nYcF82tu2YOaZBxxqI3KHz8gG0R4wZQl9r+MJrgbz7MlfzDMU8jid7vTwE/QZ9B70wjJHXD4g55IO+gcYcv/SShM5LTblG+V0G/VNWs6t313BlHs0zNHMTz1TqZRtUB70GbRnGvAe9I+aQD6x4HEckCZ2XfdCCMmaDmEP+VM0yeHcNV+bRPLNmbsuTvV7mccuVMYF9jy4OiRUvDL1HWsD6XuTKnQHtano7OeY5MccJ6KmD956FuJmb8syauS1P1nqRvdAv0KPItZahws8NE5cZdpWkwM6V5n3BMIbqdS5B4wG+ZF2Zm/LMknkSnmz1otvCP4q7w1WhNMnXzIBcd6OolxFcvT+xCbf1Owr6G+i4xYW5Kc8QzG14stVLRehP+at4zBGNOdzO04okq1rn5RXoUwK/sg/cCfCyfZmreYZkTvFkq5cfBGT1WKSO/dAgFKnOS0OBFOdXflU/CbCL+jJveCwubuYUT5Z6eQtqEve/gBYjf2+C3gxIkeq87CIYG7/NmNzTCg7map4hmVM8veulhJX/gBizojz4K3PT7gMs6mUcz+ja2LeZ/Mp7z/DY43OAAvVlbsozBHMbnt71Io8GlmLGlPHrrB9XxM/USMYvPOqlgztQmRhzg039AR79hAhf5qY8QzC34TlI9VJEEfxxC/wrYRgLXfPhAAABCXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bXN1cD48bWk+RTwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPkI8L21pPjxtc3VwPjxtaT5EPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bWk+QTwvbWk+PG1zdXA+PG1pPkI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5EPC9taT48bXN1cD48bWk+RTwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+S4hp4AAAAABJRU5ErkJggg==)
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C . Prove that
![A E squared plus B D squared equals A B squared plus D E squared](data:image/png;base64,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)
Maths-General
Maths-
A square technology chip has an area of 25 square centimetres. How long is each side of the chip ?
A square technology chip has an area of 25 square centimetres. How long is each side of the chip ?
Maths-General