SOLUTION: I need help with the following word problem: A large plywood box has a volume of 324 ft3. Its length is 12 ft greater than its height, and its width is 3 ft less than its height. W
Question 706433: I need help with the following word problem: A large plywood box has a volume of 324 ft3. Its length is 12 ft greater than its height, and its width is 3 ft less than its height. What are the dimensions of the box?
ok i know the volume of a box is found by l*w*h
the length here: H+2
the with would be: H-3
and the hight is just: H
but i don't think it would be right to do: (H)*(H-3)*(H+2)=324 Found 2 solutions by ankor@dixie-net.com, nerdybill:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A large plywood box has a volume of 324 ft3. Its length is 12 ft greater than its height, and its width is 3 ft less than its height.
What are the dimensions of the box?
:
That's the way you do it, it would be
(h+12)*(h-3)* h = 324
FOIL
(h^2 - 3h + 12h - 36) * h = 324
(h^2 + 9h - 36) * h = 324
h^3 + 9h^2 - 36h - 324 = 0
We can group factor this
h^2(h+9) - 36(h+9)
Factor out (h+9)
(h+9)(h^2-36) = 0
we are only interested in the positive solution
h^2 = 36
h = 6 ft is the height
then
L = 18, W = 3 ft
:
Check: 18 * 3 * 6 = 324
You can put this solution on YOUR website! the length here: H+12
the with would be: H-3
and the hight is just: H
.
(H)*(H-3)*(H+12)=324
now, we FOIL:
(H)*(H^2+9H-36)=324
H^3+9H^2-36H=324
H^3+9H^2-36H-324 = 0
then, we group:
(H^3+9H^2)-(36H+324) = 0
H^2(H+9)-36(H+9) = 0
(H+9)(H^2-36) = 0
H = {-9, -6, 6}
Throw out the negative solutions (extraneous) leaving:
H = 6 feet (height)
.
width:
H-3 = 6-3 = 3 feet
.
length:
H+12 = 6+12 = 18 feet
