Question

The perimeter of a rectangle is 182 ft. The width is two more feet than the length . Find the length and width.

Answer 1

Let's call the width
`w` and the length
`l` based on this, we can make two equations based on the first and second sentences in the problem.

`w = l + 2`

`2l + 2w = 182`

If we substitute
`l + 2` for
`w` into the second equation, we can make the following:

`2l + 2(l + 2) = 182`

• Substitute

`2l + 2l + 4 = 182`

• Use the Distributive Property

`4l + 4 = 182`

• Combine like terms

`4l = 178`

• Subtract 4 from both sides

`l = (178)/(4) = (89)/(2)`

• Divide both sides by 4 and simplify

Now, let's find
`w`:

`w = l + 2 = (89)/(2) + 2 = (93)/(2)`

The length of the rectangle is
`\boxed{(89)/(2) \,\textrm{ft}}` and the width of the rectangle is
`\boxed{(93)/(2) \,\textrm{ft}}`.