the area inside the frame is 180 square cm. find the width of the frame

Question

the lenght of a rectangle frame is 3cm more than the width. the area inside the frame is 180 square cm. find the width of the frame

Answer 1

let w stand for the width, then length = w+3 (3 more than width)

area is length times width.  in terms of w, area = w(w+3)

know that area = 180

so w(w+3) = 180

distribute on the left w^2 + 3w = 180

set = 0 and factor w^2 + 3w - 180 = 0

(w-12)(w+15) = 0

so w = 12 or -15

it must be 12 since you can't have a negative length.

therefore w = 12 and length = w+3 = 15

rectangle is 12 x 15 cm