Question

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}$ cm, then area of the triangle is

(a) $24\sqrt{2}c{m}^2$

(b) $24\sqrt{3}c{m}^2$

(c) $48\sqrt{3}c{m}^2$

(d) $64\sqrt{3}c{m}^2$

Answer 1

It is given the perimeter of a square ABCD is equal to the perimeter of triangle PQR.

The measure of the diagonal of the square is given .We are asked to find the area of the triangle

In square ABCD, we assume that the adjacent sides of square be a.

Since, it is a square then

By using Pythagorean Theorem

Therefore, side of the square is 12 cm.

Perimeter of the square ABCD say P is given by

Side = 12 cm

Perimeter of the equilateral triangle PQR say P₁ is given by

The side of equilateral triangle PQR is equal to 16 cm.

Area of an equilateral triangle say A, having each side a cm is given by

Area of the given equilateral triangle having each equal side equal to 4 cm is given by

a = 16 cm

Therefore, the answer is (d).