Problema Solution
A large plywood box has a volume of 1440 ft3. Its length is 18 ft greater than its height, and its width is 8 ft less than its height. What are the dimensions of the box?
Answer provided by our tutors
let
l = length, l>0
w = width, w>0
h = height, h>0
V = 1440 ft^3 the volume of the box and V = l*w*h
l*w*h = 1440
length is 18 ft greater than its height
l = h + 18
width is 8 ft less than its height
w = h - 8
by solving the system of equations
l*w*h = 1440
l = h + 18
w = h - 8
we find and consider only the positive solutions
l = 30 ft
w = 4 ft
h = 12 ft
The dimensions of the box are 30 ft, 4 ft and 12 ft.