The area of 2 rectangles is 238 cm, the width of the first is 8 cm, and the second

The area of 2 rectangles is 238 cm, the width of the first is 8 cm, and the second is 2 cm less than the width of the first. The lengths of the rectangles are the same.

Let’s determine the width of the second rectangle, knowing that it is 2 centimeters less than the width of the first:

8 – 2 = 6.

Knowing that the area of a rectangle is equal to the product of its length and width, and the lengths of the rectangles are equal, then the sum of their areas can be expressed as the product of the length of any rectangle by the sum of their widths. That is, S1 + S2 = a1b1 + a2b2 = a1 (b1 + b2) for a1 = a2. Hence the length of any of these rectangles is:

238 / (8 + 6) = 17.

Answer: The length of any of these rectangles is 17.