Question

The length of a rectangle is 5 yd longer than its width.If the perimeter of the rectangle is 70 yd, find its length and width.

Answer 1

Data and background

• The length (l) of a rectangle is 5 yd longer than its width (w).

,

• The perimeter (P) of the rectangle is 70 yd.

,

• The perimeter (P) of a rectangle is given by:

`P=2w+2l`

where w represents the width and l the length.

Procedure

We have to build two equations with the information given.

• Equation 1

`70=2w+2l`

• Equation 2

`l=w+5`

Then, we have to replace the isolated expression of l from equation 2 in equation 1:

`70=2w+2(w+5)`

Simplifying the parenthesis:

`70=2w+2w+10`

Adding similar terms:

`2w+2w=70-10`
`4w=60`
`w=(80)/(4)`
`w=15`

Now that we know the value of w, we can calculate the value of l with equation 2:

`l=15+5`
`l=20`

Answer:

• Width: 15yd

,

• Length: 20yd