# A triangle and a square have the same perimeters. The sides of the triangle are 7cm

A triangle and a square have the same perimeters. The sides of the triangle are 7cm, 8cm and 9cm. What is the area of the square?

Find the perimeter of the triangle. The perimeter of a triangle is equal to the sum of the lengths of its three sides.

P = a + b + c.

P = 7 + 8 + 9 = 24 (cm)

We have the perimeter of the triangle equal to the perimeter of the square. The perimeter of a square is the sum of its four sides, and the sides of the square are all the same. So, to find the length of a side of a square, you need to divide its perimeter into its 4 sides.

a = P: 4;

a = 24: 4 = 6 (cm)

The area of a square is equal to the square of its side.

S = a ^ 2;

S = 6 ^ 2 = 36 (cm ^ 2).

Answer. 36 cm ^ 2.

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