The area of the rectangle is 616 m² and its length is 28 m.

The area of the rectangle is 616 m² and its length is 28 m. Find the area of such a square. whose perimeter is equal to the perimeter of the rectangle.

Solution.

1. The area of a rectangle can be found by the formula S = a * b, where S is the area, a is the length, b is the width. Knowing the area and length, we find the width:

616 = 28 * b;

b = 616/28 = 22 (m).

2. Find the perimeter of this rectangle:

P = 2 * (a + b) = 2 * (28 + 22) = 2 * 50 = 100 (m).

3. Since the perimeter of the square is equal to the perimeter of the rectangle, then by the formula for the perimeter of the square P = 4 * and we find the side of the square:

100 = 4 * a;

a = 100/4 = 25 (m).

4. Find the area of a square with a side of 25 m by the formula S = a ^ 2:

S = 25 ^ 2 = 625 (m²).

Answer: the area of the square is 625 m².