The square and the rectangle have equal areas, the adjacent sides of the rectangle are 3cm and 12cm

The square and the rectangle have equal areas, the adjacent sides of the rectangle are 3cm and 12cm. Find the perimeter of the square.

First of all, we calculate the area of a rectangle with sides of 3 cm and 12 cm, multiplying the sides by each other:

S = 3 * 12 = 36 (cm²).

By the condition of the problem, the area of the rectangle is equal to the area of the square, respectively, the area of the square is also 36 cm².

Therefore, the length of the side of the square is 6 cm, since the area of the square is equal to the length of its side squared.

Now we calculate the perimeter of a square with a side of 6 cm by multiplying the length of its side by the number of sides, that is, by 4:

6 * 4 = 24 (cm).

Answer: the perimeter of the square is 24 cm.