The rectangle and the square have the same perimeters, equal to 24 cm, the length of the rectangle is 2

The rectangle and the square have the same perimeters, equal to 24 cm, the length of the rectangle is 2 times its width. Find the areas of a rectangle and a square how to correctly arrange.

The perimeter of the square is 24 cm, all sides of the square are equal (there are 4 of them), which means that the length of the side of the square is 24: 4 = 6 (cm).

To find the area of ​​a square, you need to square the side of the square:

Sq = a² = 6² = 36 (cm²).

The length of the rectangle is 2 times its width. Let the width be x, then the length is 2x. The perimeter of a rectangle is the sum of two lengths and two widths:

(x + 2x) * 2 = 24.

3x * 2 = 24.

6x = 24.

x = 24: 6 = 4 (cm) – the width of the rectangle.

2 * 4 = 8 (cm) – the length of the rectangle.

The area of ​​a rectangle is equal to the product of length and width:

Spr = a * b = 4 * 8 = 32 (cm²).

Answer: the area of ​​the square is 36 cm², the area of ​​the rectangle is 32 cm².