You are given two rectangles with equal perimeters. The first rectangle is 12 cm long and 7 cm wide.

You are given two rectangles with equal perimeters. The first rectangle is 12 cm long and 7 cm wide. The second rectangle is 5 cm wide. Find the length of the second rectangle.

The perimeter of the rectangle is calculated using the formula:
P = 2 * (a + b) where P is the perimeter, a is the length, b is the width.

So the perimeter of the first rectangle is:
1) P = 2 * (a + b) = 2 * (12 + 7) = 2 * 19 = 38 (cm) perimeter of the first rectangle.

Knowing the perimeter and width of the rectangle, you can find its length by the formula:
a = P / 2 – b

The perimeters of the rectangles are equal, the width of the second rectangle is 5cm, so its length is:
2) a = P / 2 – b = 38/2 – 5 = 19 – 5 = 14 (cm) the length of the second rectangle.

Answer: 14cm.