Question

The width of a rectangle is 6 cm less than its length. If its perimeter is 80 cm then its lengths (in cm) and area (in cm²) are respectively

Answer 1

Start by stating the given info as mathematical expressions:

1. "The width of a rectangle is 6 cm less than its length."

`w=l-6`

2. "Its perimeter is 80 cm."

`P=80`

Using the formula for perimeter (
`P=2l+2w`) we can show:

`80=2l+2w`.

We now have 2 equations in 2 unknowns and can solve by substitution:

`80=2l+2w`

`80=2l+2(l-6)`

`80=2l+2l-12)`

`92=4l`

`l=23`

The length is 23cm.

Having the length w can then find the width:

`w=l-6`

`w=23-6`

`w=17`

The width is 17cm.

And finally the area:

`A=lw`

`A=(23)(17)`

`A=391`

The area is
`391cm^(2)`.

As a check we can use the known perimeter:

`80=2l+2w`

`80=2(23)+2(17)`

`80=46+34`

`80=80` Checks true.