The square and the rectangle have the same perimeter-36 cm. The area of which figure is larger

The square and the rectangle have the same perimeter-36 cm. The area of which figure is larger if the length of the rectangle is 10 cm.

Let a be the length of the rectangle equal to 10 cm.
The perimeter of the rectangle is P = 2 * (a + b).
From here we calculate b:
2 * (10 + b) = 36.
2 * 10 + 2 * b = 36.
2 * b = 36 – 20.
b = 16/2 = 8 cm.
The perimeter of the square is P = 4 * c.
Find the side of the square with:
c = P / 4.
c = 36/4 = 9 cm.
Square area: S = a ^ 2 = 9 ^ 2 = 81 cm ^ 2.
Area of the rectangle: S = a * b = 10 * 8 = 80 cm ^ 2.
Therefore, the area of the square S = 81 cm ^ 2 is greater than the area of the rectangle S = 80 cm ^ 2.

Answer: the area of the square is larger than the area of the rectangle.