Maths-
General
Easy
Question
A square is inscribed in a circle with radius
inches. What is the perimeter of the square in inches?
![](data:image/png;base64,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)
The correct answer is: 12
Diagonal of the square inscribed in a circle = the diameter of the circle (refer diagram).
Perimeter of a square = 4 × Length of its Side
Pythagoras theorem: (Hypoteneous)2 = sum of the squares of the remaining 2 sides.
Step-by-step solution:-
We are given that radius of the circle = r = ![6 space square root of 2](data:image/png;base64,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)
We know that diameter of a circle = d = 2 × r
![equals 2 cross times 6 square root of 2](data:image/png;base64,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)
![therefore d equals 12 square root of 2](data:image/png;base64,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)
∴ in the adjacent diagram, BD =
units .------------------. (equation i)
Now, we know that adjacent sides of a square are perpendicular to each other, forming a right angle between the 2.
Hence, forming an equilateral triangle ABD in the adjacent figure.
Now, applying pythagoras theorem, we get-
(Hypoteneous)2 = Sum of the squares of the remaining sides
∴ (BD)2 = (AD)2 + (BD)2
∴
-------------------- (From equation i)
∴ 288 = (AD)2 + (AD)2 .-------------------------------------. (Lenghths of the sides of a square are equal)
∴ 288 = 2(AD)2
∴
= (AD)2
∴ 144 = (AD)2
∴
= AD ---------------------- (Taking square roots both the sides)
∴ ± 12 = AD
Since length of a side of a square cannot be negative,
∴ AD = 12 -------------- (equation ii)
Now, we know that perimeter of a square = 4 × length of side
∴ perimeter of ABCD = 4 × AD
= 4 × 12 --------------- (From ii)
= 48 inches
Final Answer:-
∴ Perimeter of a square inscribed in a circle with radius
inches is 48 inches.
Related Questions to study
Maths-
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What value of x satisfies the equation above?
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Maths-General
Maths-
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What positive value of x satisfies the equation above?
Maths-General
Maths-
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If (x, y) is the solution to the given system of equations, what is the value of y ?
![x plus y equals 5](data:image/png;base64,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)
![2 x equals 5](data:image/png;base64,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)
If (x, y) is the solution to the given system of equations, what is the value of y ?
Maths-General
Maths-
The table gives some values of x and the corresponding values of f(x) for polynomial function f. Which of the following could be the graph of f in the xy - plane, where y = f(x)?
x | f(x) |
-2 | -2 |
-1 | 3 |
0 | 2 |
1 | 7 |
2 | 30 |
The table gives some values of x and the corresponding values of f(x) for polynomial function f. Which of the following could be the graph of f in the xy - plane, where y = f(x)?
x | f(x) |
-2 | -2 |
-1 | 3 |
0 | 2 |
1 | 7 |
2 | 30 |
Maths-General
Maths-
The graph of
, where m and b are constants, is shown in the xy - plane. What is the value of m ?
The graph of
, where m and b are constants, is shown in the xy - plane. What is the value of m ?
Maths-General
Maths-
The half-life of a certain substance in an aquatic environment is about 150 years. Which of the following exponential functions best models the amount
, in grams, of the substance
years after 200 grams of the substance is applied to the aquatic environment? (The half-life is the length of time needed for an amount of the substance to decrease to one-half of that amount.)
The half-life of a certain substance in an aquatic environment is about 150 years. Which of the following exponential functions best models the amount
, in grams, of the substance
years after 200 grams of the substance is applied to the aquatic environment? (The half-life is the length of time needed for an amount of the substance to decrease to one-half of that amount.)
Maths-General
Maths-
![L minus S square root of 1 minus fraction numerator v to the power of 2 end exponent over denominator c to the power of 2 end exponent end fraction end root](data:image/png;base64,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)
When the speed of an object approaches the speed of light, its length as seen by an observer changes. When the object is stationary relative to an observer, its length is
, and when the same object is moving at speed
relative to the observer, its length is
. The formula above expresses
in terms of
, and
, the speed of light. Which of the following gives the speed of the object in terms of the other quantities?
![L minus S square root of 1 minus fraction numerator v to the power of 2 end exponent over denominator c to the power of 2 end exponent end fraction end root](data:image/png;base64,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)
When the speed of an object approaches the speed of light, its length as seen by an observer changes. When the object is stationary relative to an observer, its length is
, and when the same object is moving at speed
relative to the observer, its length is
. The formula above expresses
in terms of
, and
, the speed of light. Which of the following gives the speed of the object in terms of the other quantities?
Maths-General
Maths-
![x to the power of 2 end exponent minus 14 x plus 40 equals 2 x plus 1](data:image/png;base64,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)
What is the sum of the solutions to the given equation?
![x to the power of 2 end exponent minus 14 x plus 40 equals 2 x plus 1](data:image/png;base64,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)
What is the sum of the solutions to the given equation?
Maths-General
Maths-
What is the
-intercept of the graph of
in the
-plane?
What is the
-intercept of the graph of
in the
-plane?
Maths-General
Maths-
What is the area, in square units, of the figure shown?
![](data:image/png;base64,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)
What is the area, in square units, of the figure shown?
![](data:image/png;base64,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)
Maths-General
Maths-
![fraction numerator 4 x plus b over denominator 2 end fraction equals 2 x plus 8](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAjCAYAAABb2B7bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAq1JREFUeNrtmkFIFUEcxodHPEQkkIgID4J4kHd4lw4iEiFIdAh5BB6kk3jpEBFdPISEiOAhOkiXiOgQIYiIRIQQIh08CCLRwUPQqUN0DYnHEtQ3+AmPZbedGWfGXf3/4AN39rHvsd/OzP//rUqZcRv6q8rDb6imBK/0QAclMnoQ+iK2+OcFNBPYaJtrt6AVscUvo9BWgRn6IVjKGF/gOd9GP4EeQ/PQD6gNbUNXxS436lwi+w3M2IeudBxPQ88DzehV6Bs0C/Vyr34ms9wdPUvvG5pxizdbM96xCoQw+ivUSI1dhH6JZfY0oR1LMz5CN6DP0CUDY4uURY0Vd5ouMdqNXVa3NkY/hBI+JKGKsWHux2lGHFYRwWG26aJtjcv3VECj9bVfZ4w/gubEtrAt0AD0Dupmz71nsHS7Gr3MQi+raJSqO6DRl6EPKWN1ivYmkNHrLMbGedzHsWmxJ5zRdd7kvozPrrAS981PaIJm/2Hh14qcK6yx8Ev4/XdL4k83V7xDZgubOd4IBnxindDD4wa7k6kS/LZX0CJ0gZNwiUW14Il+FS57t8kX2hmtaCL2+KWdMRY7Gj7sWGmOjf4u9YZbYKNyevidnHMxo2G9Pz9I/a6nMgf90MV9cDTnfMxouMmlOmEtoV/4XHd9yqumkOgXKhvQzYLPxYiGdZ3wlllCnWPX1NHLn+Z5noknfUgGaPKgwXfFiIbXc64/prIjY8GAIegl+1bTvjt0NNx2PCfkoAurVfaqymDWx4qGD3JWlwb3asGS95zRRcSOhu/Q7DG2VTX+rffoe2Kb3739mNOIhjWTbOcSLte68m7FvkFlzogFj5Q5IxYCEzIjFkqGlP7ngP9lxMIZoSgjFs4AphmxUGFsMmKhothkxEJFscmIhQpjmhELFee0/jlAIP8An7kH9BUD7tQAAAC/dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93Pjxtbj40PC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5iPC9taT48L21yb3c+PG1uPjI8L21uPjwvbWZyYWM+PG1vPj08L21vPjxtbj4yPC9tbj48bWk+eDwvbWk+PG1vPis8L21vPjxtbj44PC9tbj48L21hdGg+sVAaxgAAAABJRU5ErkJggg==)
In the given equation,
is a constant. If the equation has infinitely many solutions, what is the value of
?
![fraction numerator 4 x plus b over denominator 2 end fraction equals 2 x plus 8](data:image/png;base64,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)
In the given equation,
is a constant. If the equation has infinitely many solutions, what is the value of
?
Maths-General
Maths-
Which of the following is an equation of the line in the
-plane that contains the points
and ![left parenthesis 5 , 15 right parenthesis ?](data:image/png;base64,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)
Which of the following is an equation of the line in the
-plane that contains the points
and ![left parenthesis 5 , 15 right parenthesis ?](data:image/png;base64,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)
Maths-General
Maths-
![fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis to the power of 2 end exponent end fraction](data:image/png;base64,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)
Which of the following expressions is equivalent to the given expression, where
?
![fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis to the power of 2 end exponent end fraction](data:image/png;base64,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)
Which of the following expressions is equivalent to the given expression, where
?
Maths-General
Maths-
Which of the following is equivalent to the given expression?
Which of the following is equivalent to the given expression?
Maths-General
Maths-
Bill is planning to drive 1,000 miles to visit his family. If he plans to drive 250 miles per day, which of the following represents the remaining distance
, in miles, that Bill will have to drive to reach his family after driving for
days?
Bill is planning to drive 1,000 miles to visit his family. If he plans to drive 250 miles per day, which of the following represents the remaining distance
, in miles, that Bill will have to drive to reach his family after driving for
days?
Maths-General