Question

A rug maker is using a pattern that is a rectangle with a length of 96 inches and a width of 60 inches. The rug maker wants to increase each dimension by a different amount. Let l and w be the increases in inches and the length and width. Write and simplify an expression for the perimeter of the new pattern.

Answer 1

Increasing the length by $l$ we have the new expression for the length as $96+l$

Increasing the width by $w$, we have the new expression for the width as $60+w$

Perimeter of a rectangle is given by adding all the sides, so we have

$P = 96 + l+96+l+60+w+60+w$
$P=192+2l+120+2w$
$P = 312+2l+2w$