Maths-
General
Easy
Question
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAARCAYAAAAi5qlcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAlZJREFUeNrtWE1ERFEUvp6RkcRIRpJhJEkSo3UiSZLESKtkNmnZJkmrtEmL9knSIpIWyeySkRaRVkkiSYsx22Qkw3QO3zCue999d96bn0Yfn7zunffOd8+555x7hWgcFMEf4i2xVzQP/pQ2h7hCfBDNhz+l7Vs0Lxpe2ygx06SLr9XGAzfwTp54RowbXrbuMfcxC8RP4qEhB3YhT8arIL5ooF+dH8Rn4jmx20bbBPGROII8FSKm8LKo5qPD+Gi/wbBydBAXiS/EVcX8PuIlDK0lksT9AHUuEO9stN1rIo4N29F89Jh4AHo1rAR2apY4KUVHmthe48WPYueHA9TpoOPxrK3gUrVVFbsHu4PxhGcbBzCWkeZKSBuirFq4QJSLAHX2SOtm1PZKTCj+H0M9kLGLdkrg704FDuhCTXDLz5Xm8qLHxecg2HQZt9XpIJ1npPU02sep5g2F2AGn4cUfaW4bHNaC5xB+22bpAKF4dy0RQ54OacZtdZaYIw5W2h5dowtinqJbySs6Ajlq+HnN0gGOZnfVChylY4bOx1YnO2scxXYoCCPDUjUPISoi0rwIOhvHwgG96Lyq0U6adl4SeVkHvzr7Ecy+wRGyJeVMN9EpCwdwG7pXp+uAZ5fCG5TOQE6729KB4tHlgBRTRLTOAZ3E9zpdSs16OGX71clO/rIx6oo4V1ZwupHvZsrmTEltowonmKczrBWHFI7A+TrlfrZxyWXcr0520AbxyMaoceSs0nXBiaKIZHBSdkMChxrdVUQWVxEDdSy+OUVuD1LnNw5vEfGPxscvy1rWbR8SZg8AAAChdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjk8L21uPjxtc3VwPjxtaT5BRDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+PTwvbW8+PG1uPjc8L21uPjxtc3VwPjxtaT5BQjwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+sTaJdwAAAABJRU5ErkJggg==)
The correct answer is: Hence proved
Solution :-
Aim :- Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAAARCAYAAAAmE3lhAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAApBJREFUeNrtWF9EZFEcvjJGktiHJCMxsnpay1rpKZEkKyOyslZWrLX2YR+WfVo9pJeekkSS9JAhq4dkX1bWSrKsZO1Dlqx97KWHjDUyTN+PbzhO9/xp7txuM/r4Hu6Zn3vOd3/nfL/fmSC4WyiTl+AB2BM0FupOXxP4FjwKGhN1p68YNDbqQt8A+L2Bk2DUJz/sM0v/wc9g1vOl7z0yX1ZYALfAbkN8Jz00G8MHKDtYC60l8B94Cu5Qj5e+YfA3+JT+lQKnwROwwzHxcxaflOF3KUjHmj/KQt5xseNa/ENwN2TxcWMCXK2xVsEsuO6r76dh98ni5i0LewD+Ar+COUOMjG9axF8wOZWd8gVsu+UkdNANmmPQOq6MOfWVLNXdVtlXwElwClwyxMyAHyzvKPAkBlxkbwJ+Lfbx2BHjq/WjNrYBjvjqEy97EjLezXoRhn4escqOOjXESS0Ys8y9Bw5Z/Ltary97JuEN+MkRcxOtOW5gSeyaVlOcaxSL+MuC3UQ+42m4DJkwRTvrUsaODNn+4/B7mbc9oc5FNtoPi+dXo1VtSEaqbae+seoXmd0ew4kIs5s5XlJ0aytY5mwBzxJsIaV9HHTEVKM1zVN+yOIcGc3cMSp6DXVjgF6roo/WY8KUR6cSlzVN0LNtiKr1haPZ8cYg2y8V+xbhems3SZ80QbqQRwn9xXDiUaCjan0ZYaNdO4IZ5fk1uGCJz4OjyvMi+MoQu+B4V5zIedzaa6F1jQnyxh773TSfM+wkxrTboOzgVst7prXFb2sFK83Lo1jCcoK1IW/ZILXQ2k7rO1a+qReGWKhLvGDlQyxji52UDRl2DhWcK0e5xMK8yXYwSZzxghZY2tAoWov8hpngHvWFKyMT1bdtbIwRAAAAs3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj45PC9tbj48bWk+QTwvbWk+PG1zdXA+PG1pPkQ8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPj08L21vPjxtbj43PC9tbj48bWk+QTwvbWk+PG1zdXA+PG1pPkI8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tYXRoPl2mgmgAAAAASUVORK5CYII=)
Hint :- let the side of equilateral triangle be x , then we get height of equilateral
triangle as
.Now , Find length of DE and apply pythagoras theorem in
Right angle triangle ADE to find length of AD in terms of AB.
Explanation(proof ) :-
In equilateral triangle all sides are equal
Let , AB = BC = CA = x
Given BD = ⅓ BC = x/3
In equilateral triangle ,the altitudes and medians coincide
so,AE is median also i.e E is midpoint of BC
BE = x/2
From diagram ,DE = BE - BD ![equals x over 2 minus x over 3 equals x over 6](data:image/png;base64,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)
We get height of equilateral triangle when side x is![fraction numerator x square root of 3 over denominator 2 end fraction](data:image/png;base64,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)
Applying pythagoras theorem on triangle ADE
We get ![A D squared equals D E squared plus A E squared equals open parentheses x over 6 close parentheses squared plus open parentheses fraction numerator x square root of 3 over denominator 2 end fraction close parentheses squared](data:image/png;base64,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)
![∣ A D squared equals x squared over 36 plus fraction numerator 3 x squared over denominator 4 end fraction equals fraction numerator 28 x squared over denominator 36 end fraction equals 7 over 0 x squared](data:image/png;base64,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)
![](data:image/png;base64,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)
Substitute x by AB as x = AB
![A D squared equals 1 over 9 A B squared not stretchy rightwards double arrow 9 A D squared equals 7 A B squared](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
In the figure, find the value of x.
![](data:image/png;base64,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)
In the figure, find the value of x.
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Simplify √12 - √48 +√1323
Simplify √12 - √48 +√1323
Maths-General
Maths-
In
, the bisectors of
and
intersect each other at O. Prove that
![90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAjCAYAAADyrNZPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAApdJREFUeNrtmkFkXEEYx0c8FVWhp7WqQkRED71UVfRQpaoqqkJE9NBDyKGnHHqr6KHK6qmqSkRV5VBiRVVUqVpROYSqqh6qRM655BBRK8L2//F/PNOZl3nZ3feSt9+fPzuz3+bxm5lvvpkXY8qvEXge/mFUuWsJnoVbiqI4KXyFr/BVCl/hqxR+d1SDd+maws8X/Dpcpb8WOAA9B3+P0GNVuQLKBv9mu3/gGmdmE/4L1+EhR9wA/AreoBfYd1zhtxzupITFu4C4ubSR+wVfhvvgCJ6Bf8MVK/YLfCfRHmdfSNpZLzjvd1oy8XbgK4fETcH75Pqfvnlm+ST8zGq/cMQ9h6dTBmCPrh2zdNGO3gaCPwv/hD/Dd10BB54fyir4nmjXPfntOr/rlY1yKRB8vDpkYt6HX7oCNuFLjv5B5v9Y8sBTjjjp2+4R+PUM4MfgVX6ukLMzvWxx0+2jxznr9wNWiLHiyghfmKxkAB8xnZ9P9AnPUV+102C1I16Gh62Znwa/2cXqJLRaaR3RISCzgBc9hh9afU/hB6Eg+llOxtr2pJ3+EqediKkjC/hRa69MTvAPoQ+WjfSJle9ueUrVMm64MtE+ZgRveF7yrTJvyWkcy+Rcoj0BLzri3qSUmicVvqzmT0cAP8vS2yc5kN22D04TiZQiwOetw1SsBk9rEeMfwWslu5M5TSZZwVdZ059JiZmxB+cGoR7w+C+jczHl0PA6cQ2xcMjDTqIaGTfs+HphmVVimmRi/zEl11XuQ7vMs/KvI/eMKhetcR+KV+UF3i1NK5piNMicrCpITUVQjMaYelQF1O0b3IhVOUrK4/emA6/7VNk0RPDDiiJfyQXXIk+sqhxV4YkzUhT5a9V4Xlyouq92Xp7kon+pXsa6oKW7/QAAAMV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bW4+OTA8L21uPjxtbz4mI3gyMjE4OzwvbW8+PC9tc3VwPjxtbz4rPC9tbz48bWZyYWM+PG1uPjE8L21uPjxtbj4yPC9tbj48L21mcmFjPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyMjIwOzwvbWk+PG1pPkE8L21pPjwvbWF0aD7BFYtfAAAAAElFTkSuQmCC)
In
, the bisectors of
and
intersect each other at O. Prove that
![90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,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)
Maths-General
Maths-
and are the medians of a
right angled at . Prove that
.
and are the medians of a
right angled at . Prove that
.
Maths-General
Maths-
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,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)
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √50 - √98 + √162
Simplify √50 - √98 + √162
Maths-General
Maths-
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 ?
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 ?
Maths-General
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
.
![](data:image/png;base64,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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