Question

Find the length and width of a rectangle whose perimeter is 42 feet and whose area is 98

square feet.

Answer 1

The perimeter formula is p=2w + 2l
The area formula is a=wl

So if the perimeter is 42 the formula would be. 42=2w+2l

If the area is 98 the the formula would be
98 = wl

Take 42=2w+2l and divide both sides by 2

21=w+l
Solve for w by subtracting l

21-l=w. The substitute into the area formula

98=wl
98 = (21-l)l
98=21l-l^2
l^2-21l+98=0. Now factor

(l-7)(l-14)=0

If length is 7 then width is 14. Or if the length is 14. then the width is 7