The perimeter of the square is equal to the perimeter of the rectangle, which is 12 cm

The perimeter of the square is equal to the perimeter of the rectangle, which is 12 cm long and 48 cm2 in area. Find the side length of the square.

S of a rectangle = a * b, where a and b are the sides of this rectangle.
48 = 12 * b.
b = 48: 12.
b = 4.
4 (cm) – the width of the rectangle.
P of a rectangle = 2 * (a + b), where a and b are the sides of this rectangle.
P rectangle = 2 * (12 + 4).
P rectangle = 2 * 16.
P rectangle = 32.
32 (cm) – the perimeter of this rectangle.
P of the square = 4 * a, where a is the side of the square.
Since in the condition P of the square = P of the rectangle, we find the side of the square, then we get:
32 = 4 * a.
a = 32: 4.
a = 8.
8 (cm) – side of the square.
Answer: 8 cm.