SOLUTION: I am trying to solve a volume problem. The volume of a box is 1755 cubic feet. The width of the box is 9 feet and it's height is 2 feet more than its length. I have to find the

Question 377127: I am trying to solve a volume problem. The volume of a box is 1755 cubic feet. The width of the box is 9 feet and it's height is 2 feet more than its length. I have to find the height of the box. I know the formula for volume is v=lwh, but the 2 feet more than the length is throwning me off. Can you please help????
Thanks,
Denise
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
write an equation for each statement:
;
The volume of a box is 1755 cubic feet.
L * W * H = 1755
:
The width of the box is 9 feet
W = 9
:
and it's height is 2 feet more than its length.
H = (L+2)
:
Replace W with 9, and H with (L+2)
L * 9 * (L + 2) = 1755
9L(L+2) = 1755
9L^2 + 18L = 1755
9L^2 + 18L - 1755 = 0
Simplify, divide b6 9
L^2 + 2L - 195 = 0
Factors to
(L - 13)(L + 15) = 0
Positive solution
L = 13 ft is the length
then
H = 13 + 2
H = 15 ft is the height
:
:
Check solution by finding the vol with these values:
13 * 9 * 15 = 1755, confirms our answers

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