# Find the perimeter of a rectangle whose area is 160 and the aspect ratio is 2: 5

May 31, 2021 | education

| We are given a rectangle. It is known that its area is 160 sq. units. It is also known that its aspect ratio is 2: 5.

To calculate the perimeter of the rectangle, we will use the formula:

P = 2 (a + b).

We need to find the length of the sides of the rectangle. Let’s denote by x the coefficient of similarity and write the sides of the rectangle as 2x and 5x.

Area formula:

S = a * b;

Substitute the values and find x:

2x * 5x = 160;

10x ^ 2 = 160;

x ^ 2 = 16;

x = 4.

The sides of the rectangle are 2 * 4 = 8 and 5 * 4 = 20.

P = 2 (8 + 20) = 2 * 28 = 56.

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