The length of the bottom of the rectangular pool is 5 times its width and the width

The length of the bottom of the rectangular pool is 5 times its width and the width is 20 meters less than the length. Find the area of the pool bottom.

Let the length of the pool be l, its width b.

Since the length is 5 times the width, we can write: l = 5 * b.

On the other hand, the width is 20 m less than the length, which means b = l – 20.

We have a system of equations:

1) l = 5 * b;

2) b = l – 20.

Let us express l through b from the second equation and substitute the resulting value into the first:

l = b + 20;

b + 20 = 5 * b;

4 * b = 20;

b = 20/4 = 5 m – the width of the bottom of the pool, hence the length of the bottom l = 5 * 5 = 25 m.

The area of the pool bottom is defined as the product of width and length: S = l * b = 25 * 5 = 125 m2.