Question

The length of a rectangular carpet is 3 feet longer than twice its width. If the area of

the carpet is 65 square feet, what is its perimeter?

Answer 1

`Perimeter = 45ft`

Explanation:

Given

Represent the Length as L and the Width as W.

So, we have the following:

`L = 2W + 3`

`Area = 65`

Required

Determine the perimeter

The area of a rectangle is calculated as thus:

`Area = L * W`

Substititute 65 for Area

`65 = L * W`

Substitute 2W + 3 for L

`65 = (2W + 3) * W`

This gives:

`65 = 2W^2 + 3W`

Equate to 0

`2W^2 + 3W - 65 = 0`

Expand:

`2W^2 + 10W - 13W - 65 = 0`

Factorize:

`2W(W + 5) - 13(W + 5) = 0`

`(2W - 13)(W + 5) = 0`

`2W - 13 = 0\ or\ W + 5 = 0`

`2W = 13\ or\ W = -5`

`W = (13)/(2)` or
`W = -5`

But width can't be less than 0.

So:

`W = (13)/(2)`

`W = 6.5`

Recall that:

`L = 2W + 3`

`L = 2 * 6.5 + 3`

`L = 16`

The perimeter is calculated as thus:

`Perimeter = 2 * (L + W)`

`Perimeter = 2 * (16 + 6.5)`

`Perimeter = 45ft`