The height of a box is 7 inches. its length is 6 inches more than its width. find the length if the volume is 280
cubic inches.

H = 7
l = w + 6
V = 280

V = lwh

Plug in what we know:

280 = (w + 6)(w)(7)

Distribute W into the first parenthesis:

280 = (w^2 + 6w)(7)

Distribute 7:

280 = 7w^2 + 42w

Divide 7 to both sides:

40 = w^2 + 6w

Subtract 40 to both sides:

w^2 + 6w - 40 = 0

Factor:

(w - 4)(w + 10) = 0

Therefore, w = 4.

Plug this back into the equation for the length:

l = w + 6

l = 4 + 6

l = 10