Question

Walter is making an open-top box. The length is 6 inches greater than the width, and the height is 2 inches. The area of the rectangular sheet of material that will be folded to make the box is 280 square inches.

What is the length of the box in inches?

(I really don't know where to start)

Answer 1

just start by listing the facts:

width=w
length=w+6
height=2

area is the 4 sides + bottom
= 2(width*height)+2(length*height)+(length*width)
= 2(2w)+2(2(w+6))+w(w+6)
= 4w + 4w+24 + w^2+6w
= w^2 + 14w + 24

So, now we know that

w^2+14w+24 = 280
w^2+14w-256 = 0

Solve that for w, and the length is w+6