The perimeter of the square is equal to the perimeter of the rectangle. The area of the rectangle is 24m, and one side

| September 22, 2021 | education

The perimeter of the square is equal to the perimeter of the rectangle. The area of the rectangle is 24m, and one side is 1.5 times smaller than the other. Find the side of the square.

Let one of the sides of this rectangle be equal to x, then the other is equal to 1.5x.

The area of a rectangle is equal to the product of its two adjacent sides:

S = x * 1.5x = 1.5x ^ 2.

Knowing that the area is 24, we find the sides of the rectangle:

x ^ 2 = S / 1.5 = 24 / 1.5 = 16;

x = √16 = 4 cm – one of the sides of the rectangle.

1.5x = 1.5 * 4 = 6 cm – the second side of the rectangle.

The perimeter of this rectangle: P = 4 * 2 + 6 * 2 = 20 cm.

The perimeter of the square is equal to the perimeter of the rectangle, so the side of the square is:

a = P / 4 = 20/4 = 5 cm.



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