# The perimeter of the triangle is 96 cm and it is eight times larger than one of the sides of the rectangle.

August 28, 2021 | education

| **The perimeter of the triangle is 96 cm and it is eight times larger than one of the sides of the rectangle. Find the area of the rectangle.**

We decide by action.

Let’s find the length of one of the sides of the rectangle using the condition of the problem:

1) 96: 8 = 12 (cm) – the length of the side of the rectangle.

We use the formula for the perimeter of a rectangle: P = 2 • (a + b). Suppose we know, for example, a = 12 cm. Small equation:

2) 96 = 2 • (12 + b);

12 + b = 96: 2;

12 + b = 48;

b = 48-12;

b = 36 (cm) – the length of the second side of the rectangle.

It remains to find its area: S = a • b.

3) S = 12 • 36 = 432 (cm2).

Answer: 432 cm2.