volume of a box

[PepprRN]

Help!!
A large box has a volume of 180ft^3. Its length is 9ft greater than its height and its width is 4ft less than its height. What are the dimensions of the box?

I have 180=(h+9)(h-4)(h) and I keep coming up with h=4 which would mean the height is 0...not possible. Help!!

[MAS1]

Originally Posted by PepprRN

Help!!
A large box has a volume of 180ft^3. Its length is 9ft greater than its height and its width is 4ft less than its height. What are the dimensions of the box?

I have 180=(h+9)(h-4)(h) and I keep coming up with h=4 which would mean the height is 0...not possible. Help!!

h(h + 9)(h - 4) = 180
(h^2 + 9h)(h - 4) = 180
h^3 - 4h^2 + 9h^2 - 36h = 180
h^3 + 5h^2 - 36h = 180
h^3 + 5h^2 - 36h - 180 = 0


Let's try 6 as a solution.

(6)^3 + 5(6)^2 - 36(6) - 180 = 0
216 + 180 - 216 - 180 = 0
0 = 0

It turns out the other 2 roots are -6 and -5 (you can check by plugging them into the equation) so we will use h = 6 ft for the height.

Then the length is 6 + 9 = 15 ft and width is 6 - 4 = 2 ft.

Hope this helps.