SOLUTION: A large plywood box has a volume of 240 ft^3. 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?
Question 644439: A large plywood box has a volume of 240 ft^3. 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? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Volume(V) of a box=Length(L)*Width(W)*Height(H) or V=LWH
Let H=height of the box
Then L=H+16
And W=H-1
Sooooo:
V=240 ft^3=(H+16)*(H-1)*H expanding, we get:
H^3+15H^2-16H-240=0 cubic in standard form and we can factor by grouping
(H^3+15H^2)-16(H+15)=0
H^2(H+15)-16(H+15)=0
(H+15)(H^2-16)=0
(H+15)(H-4)(H+4)=0 so:
H=-15 &
H=-4 &
H=+4----------------------answer
CK
V=240=4*20*3=240
240=240
Hope this helps---ptaylor
