# The perimeter of the rectangle is 56m², and the width is 4m. Find the area of a square whose

September 20, 2021 | education

| **The perimeter of the rectangle is 56m², and the width is 4m. Find the area of a square whose perimeter is equal to the perimeter of this rectangle.**

Apparently, 56 m², we are talking about the area of a rectangle. The area and width are known, we find the length of the rectangle:

S = a * b → a = S / b = 56/4 = 14 (cm).

Find the perimeter of this rectangle:

P = 2 * (a + b) = 2 * (14 + 4) = 2 * 18 = 36 (cm).

The perimeter of a square is found by the formula:

P = 4 * a → a = P / 4 = 36/4 = 9 (cm).

The side of the square is known, we find the area:

S = a² = 9² = 81 (cm²).

Answer: the area of the square is 81 cm².

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