The bottom of the pool is rectangular. Its width is 5 times less than its length.

The bottom of the pool is rectangular. Its width is 5 times less than its length. What is the area of the pool bottom if its length is 40 m longer than the width?

1) Let’s express the width of the rectangle in terms of the length. The problem statement says that the width is 5 times less than the length. If we say that the value is several times greater or less, then we are talking about multiplication or division. In our case, we are talking about division.
b = a / 5.
2) Express the length of the rectangle in terms of the width. The problem statement says that the length is 40 m more than the width. If the preposition “on” is used, then we are talking about subtraction or addition. In our case, we are talking about addition.
a = 40 + b.
3) Find the length and width of the rectangle. We substitute in the expression for length instead of width, b, its value and solve the equation with one unknown:
a = 40 + a / 5,
5a = 200 + a,
5a-a = 200,
4a = 200,
a = 50 m.
b = 50: 5 = 10 m.
4) Find the area of ​​the rectangle.
Let’s write the formula for the area:
S = a × b,
where S is the area, a is the length of the rectangle, b is the width.
Substituting the values ​​of the lengths of the sides of the rectangle into the formula, we find the area:
S = 50 × 10 = 500 m2
Answer: the area of ​​the bottom of the pool is 500 m².