The sum of the areas of two rectangles with the same width is 30 cm, the length of the first rectangle is 6 cm

The sum of the areas of two rectangles with the same width is 30 cm, the length of the first rectangle is 6 cm and the second is 2 cm less. Find the area of each rectangle?

Let’s denote the width of each rectangle by x cm.

By the condition of the problem, we know the lengths of both rectangles and the sum of the areas.

So, we write the equation:

6 x + (6 – 2) x = 30.

10 x = 30.

x = 3.

Thus, the width of the rectangles is 3 cm.

Let’s calculate the area of each of them:

S = 6 * 3 = 18 (cm²).

S = 4 * 3 = 12 (cm²).

Answer: the area of the first rectangle is 18 cm², the second rectangle is 12 cm².