# A rectangle and a square have the same perimeter, a rectangle is 13 cm long and 10 cm shorter

July 29, 2021 | education

| **A rectangle and a square have the same perimeter, a rectangle is 13 cm long and 10 cm shorter in width, find the area of the square.**

1. By the condition of the problem, the length of the rectangle is 13 cm.

It is known to be 10 cm shorter in width.

Determine how many centimeters the width is.

13 – 10 = 3 cm.

2. Find the perimeter of the rectangle.

P1 = 2 * (13 + 3) = 2 * 16 = 32 cm.

3. In accordance with the condition of the problem, the rectangle and the square have the same perimeter.

This means that the perimeter of the square is also P2 = 32 cm.

4. Find the side of the square.

P2 / 4 = 32/4 = 8 cm.

5. Let’s calculate the area of the square.

S = 8 * 8 = 64 cm2.

Answer: The area of the square is 64 cm2.

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