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

Start by stating the given info as mathematical expressions:

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

2. "Its perimeter is 80 cm."
     

Using the formula for perimeter () we can show:
.

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






The length is 23cm.

Having the length w can then find the width:




The width is 17cm.

And finally the area:




The area is . 

As a check we can use the known perimeter:



Checks true. 

The answer is