Question

A rectangle has a perimeter of 80 feet. Its height is 5 feet shorter than 4 times its base. What are the dimensions of this rectangle?

Answer 1

31 feet by 9 feet

Explanation:

Firstly, label the dimensions of the rectangle as variables.

Since the perimeter is 80 feet, all four sides must add up to 80

Let the height `=h`
and the base `=b`

The perimeter of a rectangle is made up of two of the base lengths and two of the height lengths.

`2b+2h=80`
`b+h=40`
`b=40-h`

From the second part of the question:

`h+5=4b`

Substituting the expression for `b`

`h+5=4*(40-h)`
`h=160-4h-5`
`5h=155`
`h=31`

Substituting this found value of `h` into the expression for `b`

`b=40-31`
`b=9`

`therefore` the dimensions of the rectangle are 31 feet by 9 feet