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.