A gift box has a value of 450 in.³. The width of the box is 4 inches less than the length. The height is twice the witdth. what is the width and inches of the gift box?

Answer 1

L = w+4
h = 2w

450 = w L h

450 = w * (w+4) * 2 w
450 = 2 w^2 (w+4) = 2 w^3 + 8 w^2

w^3 + 4 w = 225
w^2 (w+4) = 225

guess w around 200^.3 or 4.9
then w^2(w+4) = 213.8 not bad guess
try w = 5
25(9) = 225, we are there

check
w = 5
L = 9
h = 10
sure enough