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jn0r
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A thread put in the shape of a square is rearranged to form an equilateral triangle. What is the approximate percentage change in area covered by the thread?
A)15% increase
B)25% increase
C)10% increase
D)25% decrease
E)35% decrease
A)15% increase
B)25% increase
C)10% increase
D)25% decrease
E)35% decrease
siddhantmittal
28 Jan 2021, 05:05
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A thread is arranged in the form of a square
Perimeter of a square = \(4*side\)
Let's assume side of square as "a"
Length of thread = Perimeter of square = \(4*a\)
Now rearranging it in the form of equilateral triangle, the length of thread remains same
So length of thread = perimeter of equilateral triangle
Let's assume side of equilateral triangle as s
\(4*a=3*s\)
Area of square = \(a^2\)
Area of equilateral triangle =\(\sqrt{3}/4 * s^2\)
% difference = Change/Initial value * 100
We get ~22% decrease so the answer is 25% decrease
Perimeter of a square = \(4*side\)
Let's assume side of square as "a"
Length of thread = Perimeter of square = \(4*a\)
Now rearranging it in the form of equilateral triangle, the length of thread remains same
So length of thread = perimeter of equilateral triangle
Let's assume side of equilateral triangle as s
\(4*a=3*s\)
Area of square = \(a^2\)
Area of equilateral triangle =\(\sqrt{3}/4 * s^2\)
% difference = Change/Initial value * 100
We get ~22% decrease so the answer is 25% decrease
General Discussion
28 Jan 2021, 01:40
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Perimetre of sqaure = perimetre of triange => 4a=3b. (let a be the side of square and b be the side of triangle)
Now, let a=3, so b becomes 4.
By subtracting the areas, we will get = a^2-1/3*squarer3/2b*b => 9-4sqauer3.
Finding 9-4sqauer3 is what percentage of 9 gives an approximate answer of 22%.
Hence, 25 is the answer.
Now, let a=3, so b becomes 4.
By subtracting the areas, we will get = a^2-1/3*squarer3/2b*b => 9-4sqauer3.
Finding 9-4sqauer3 is what percentage of 9 gives an approximate answer of 22%.
Hence, 25 is the answer.
