The length of a rectangle is 5 times its width, which is equal to the area of this rectangle if its width is 8 cm

The length of a rectangle is 5 times its width, which is equal to the area of this rectangle if its width is 8 cm less than its length.

Let’s take for x and y the length and width of the rectangle, respectively. Since the length is 5 times the width, we get the equation:

x = 5 * y.

Since the width is 8 less than the length, we get the 2nd equation:

x – 8 = y.

Substitute the y from the 2nd equation into the 1st:

x = 5 * (x – 8);

x = 5x – 40;

4x = 40;

x = 10 cm.

Then y = 10 – 8 = 2 cm.

The area of the rectangle will be:

10 * 2 = 20 cm ^ 2.

Answer: the required area of the rectangle is 20 cm ^ 2.