Question

The width of a rectangle is 3 feet shorter than its length. The perimeter is 530 feet. Let x equal the length of the rectangle. The formula is P = 2l + 2w. What are the length and the width of the rectangle? a. Write a list of the known information and the unknown information. Write an algebraic equation to show the relationship between the knowns and the unknowns. Solve the equation.

Answer 1

1) Known information:

- The perimeter.

-
`width=lenght-3ft`

- The formula of the perimeter of the rectangle:

`P=2l+2w`

Unknown information:

- The value of the widht.

- The value of the length.

2) Equation:

`530=2l+2w\\530=2l+2(l-3)`

3)
`l=134\\w=131`

Explanation:

1. The problem gives you the perimeter, the formula of the perimeter of a rectangle and says that the width of a rectangle is 3 feet shorter than its length (
`w=l-3`), but does not give the value of the widht and the value of the lenght.

2. Based on the information given, you can write the following equation:

`530=2l+2w`

Where
`l` is the lenght and
`w` is the width.

Substitute
`w=l-3` into the equation above, then you have:

`530=2l+2(l-3)`

3. Solve for the lenght:

`530=2l+2(l-3)\\530=2l+2l-6\\536=4l\\l=134`

4. Know you can calculate the width:

`w=l-3=134-3=131`

5. Therefore, the length is 134 feet and the widht is 131 feet.