The two rectangles have the same base. The height of one rectangle is 15 cm, and the height of the other is 9 cm.

The two rectangles have the same base. The height of one rectangle is 15 cm, and the height of the other is 9 cm. Find the bases of the rectangles if the area of the first is 48 cm² larger than the area of the second.

Let us denote by the variable n the unknown dimension of the first and second rectangles.

Accordingly, we can represent the area of the first rectangle as 15n, and we can represent the area of the second rectangle as 9n.

Since from the conditions of this task we know that the area of the first figure exceeds the area of the second by 48 cm2, we write down the equation and calculate the unknown measurement:

15n – 9n = 48;

6n = 48;

n = 8.

Answer: The base of the first and second rectangles is 8 centimeters.