Find the area of a rectangle if its perimeter is 52 and the ratio of adjacent sides is 3:10.

In order to find the area of a rectangle, we need to know the lengths of the sides of this rectangle.

We know the perimeter of the rectangle P = 52, as well as the aspect ratio of the rectangle 3: 10.

The coefficient of similarity will be denoted by x, then the length of one of the sides is 3x, and the length of the second is 10x.

Let’s recall the formula for the perimeter of a rectangle:

P = 2 (a + b);

2 (3x + 10x) = 52;

13x = 26;

x = 26: 13.

x = 2.

One side is equal to 3x = 3 * 2 = 6; and the second is 10x = 10 * 2 = 20.

We are looking for the area of a rectangle using the formula:

S = a * b;

S = 6 * 20 = 120.