Question

PLZPLZPLZ HELP ME!!!

The length of a particular rectangle is 2 inches less than twice its width. If the area of the rectangle is 40 square inches, find the length and width.

(A.) length is 6 in, width is 4 in

(B.) length is 2 in, width is 2 in

(C.) length is 5 in, width is 8 in

(D.) length is 8 in, width is 5 in

Answer 1

If
`\ell` is the length and
`w` the width, then
`\ell=2w-2`.

Since the area of the rectangle is


`\ell w=40`

you have


`(2w-2)w=40\implies 2w^2-2w-40=0\implies w^2-w-20=0`

Factoring the left hand side gives


`(w-5)(w+4)=0\implies w=5,w=-4`

Obviously the width can't be negative, so
`w=5`. This means D is the answer, since it's the only option with this measure.