# Given two rectangles with equal perimeters, the first rectangle has a length of 12 cm

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

Find the perimeter of the first rectangle.

According to the condition of the problem, the length of the first rectangle is 12 cm, and its width is 7 cm, therefore, the perimeter P of this rectangle is:

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

By the condition of the problem, the perimeters of both rectangles are the same, therefore, the perimeter of the second rectangle is also 38 cm.

Find the length of the second rectangle.

Let us denote it by x.

According to the condition of the problem, the width of the second rectangle is 5 cm, therefore, we can draw up the following equation:

2 * (x + 5) = 38.

We solve the resulting equation:

x + 5 = 38/2;

x + 5 = 19;

x = 19 – 5;

x = 14 cm.

Answer: the length of the second rectangle is 14 cm.