A large plywood box has a volume of 240 ft3 Its length is 16

A large plywood box has a volume of 240 ft³. Its length is 16 ft greater than its height, and its width is 1 ft less than its height. What are the dimensions of the box?

Solution

So,the box is of the shape of a cuboid.

Volume of cuboid = length x width x height

length = 16+ height ---> l= 16 +h

width = height -01 ----> w = h-1

So, V= l*w*h = (16+h)(h-1)(h) = 240 ft^3

Solve for h : h( h-1)( h+16) = 240

h( h^2 + 15h -16) = 240

h^3 +15h^2 -16h -240 =0

On solving the above equation we get roots as h = 4 , -4, -15

Negllecting -ve roots:

So, h= 4ft ; l = 20ft ; w= 3 ft

Answer: width = 3ft