Given two rectangles with equal perimeters. The first rectangle has a length of 12cm, width 7cm.

Given two rectangles with equal perimeters. The first rectangle has a length of 12cm, width 7cm. The width of the second rectangle is 5cm. find the length of the second rectangle.

The perimeter of a rectangle P is the sum of the lengths of all four of its sides. Moreover, these sides are equal in pairs: P = 2 * A + 2 * B = 2 * (A + B).

Find the perimeter of the first rectangle:

P1 = 2 * (12 + 7) = 2 * 19 = 38 cm.

Since P1 = P2, it is not difficult to find the length of the second rectangle, knowing its width and perimeter:

A = (P – 2 * B) / 2 = (38 – 2 * 5) / 2 = 28/2 = 14 cm.