Question

The perimeter of a rectangular swimming pool is 414 meters. The length of the pool is 7 meters more than four times the width. Find the length and the width.

Answer 1

Answer: Length= 167 meters, Width= 40 meters

Explanation:

We know that perimeter is the lengths of all sides of the rectangle added together. Therefore, the formula for perimeter is
`P=2l+2w`. We can use system of equations to find length and width.

`P=2l+2w`

`l=7+4w`

The second equation comes from the fact that the length is 7 meters more than 4 times the width.

Since we know the equation of
`l`, we can use substitution to find
`l` and
`w`.

`P=2(7+4w)+2w`

`P=14+8w+2w`

`P=14+10w`

The problem gives us the perimeter to we can plug that into P.

`414=14+10w`

`400=10w`

`w=40`

Now that we know the width, we can plug it into the equation to find length.

`l=7+4(40)`

`l=7+160`
`l=167`