If perimeters of square and equilateral triangle are equal and tr

If perimeters of square and equilateral triangle are equal and tr
| If perimeters of square and equilateral triangle are equal and triangle has area of 49.26 cm2, what will be the area of square?

A. 64 cm<sup>2</sup>

B. 72 cm<sup>2</sup>

C. 81 cm<sup>2</sup>

D. 108 cm<sup>2</sup>

Please scroll down to see the correct answer and solution guide.

Right Answer is: A

SOLUTION

Let side of square be x and that of triangle be y

∴ 4x = 3y (∵ perimeters are same)

As we know area of equilateral triangle is given by

\(A = {\rm{\;}}\frac{{\sqrt 3 }}{4}{y^2}\)

⇒ 49.26 = (√3 × y2)/4

⇒ y2 = 49.26 × 4 /√3

⇒ y2 = 113.761`

⇒ y = 10.67 cm

Now as 4x = 3y

∴ x = (3 × 10.67)/4

⇒ x = 8 cm

Area of square is given by

A = x2

⇒ A = 82 = 64 cm2

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