Question

The length of a rectangle is 5 more than the width. If the perimeter is 18 meters, what are the the length and width?

Write an algebraic expression used to solve the problem but do not solve

Answer 1

Let
`x` be the length of the rectangle, and let
`y` be its width. The perimeter of a rectangle is the sum of all its side lengths:


`P=2x+2y`

(since there are two sides of length
`x` and two sides of length
`y`)

You know the perimeter is 18 meters, so the equation above is


`18=2x+2y`

Now, you also know that the length of the rectangle is 5 meters longer than the width, which means
`x=y+5`, or equivalently,
`x-y=5`. So you have two equations depending on
`x` and
`y`:


`\begin{cases}2x+2y=18\\x-y=5\end{cases}`

From here, you could substitute the second equation into the first to get an equation only in terms of the width
`y`. Since
`x=y+5`, you have


`2(y+5)+2y=18`

and solve for
`y` from there (but you're not asked to do so).