A rectangle, the adjacent sides of which are 42 cm and 14 cm, and the square have equal perimeters.

A rectangle, the adjacent sides of which are 42 cm and 14 cm, and the square have equal perimeters. Find the side length of the square.

Let’s find the perimeter of the rectangle based on the task data.
P (rectangle) = 2 (a + b) = 2 (42 + 14) = 84 + 28 = 112 (cm).
Knowing that the perimeters of the square and the rectangle are equal, we substitute the found perimeter of the rectangle into the formula for finding the perimeter of the square and solve the resulting equation with one unknown.
P (square) = 4a.
112 = 4a.
a = 112/4.
a = 28 (cm).
Answer: 28 cm.