Question

The length of a rectangle is 9 cm less than 4 times the width. The perimeter is 142 cm. What is the width and length?

Answer 1

The length is `55"cm"` and the width is `16"cm"`

Explanation:

Let `l` be the length of the rectangle and `w` be the width.

By the first statement, we have
`l = 4w-9`

By the second, we have
`2l + 2w = 142`

Thus we need to solve the system of equations

`{(l -4w = -9), (2l + 2w = 142):}`

Using elimination, we can subtract twice the first equation from the second to obtain

`2l + 2w -2(l - 4w) = 142 - 2(-9)`
`=> 10w = 160`
`=> w = 16`

Now we substitute that back into the first equation to get
`l - 4(16) = -9`
`=> l = 55`

Thus the length is `55"cm"` and the width is `16"cm"`