SOLUTION: I really need some help on a problem. It is a word problem and I really can NOT do them! It says.... The volume of a box is 1755 cubic feet. The width of the box is 9 feet, a

Algebra ->  Real-numbers -> SOLUTION: I really need some help on a problem. It is a word problem and I really can NOT do them! It says.... The volume of a box is 1755 cubic feet. The width of the box is 9 feet, a      Log On


   

Question 701738: I really need some help on a problem. It is a word problem and I really can NOT do them!
It says....
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 it's length. Find the height of the box.
Thank you for your help!
Melissa
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The volume of a box is V=L%2AW%2Ah where L=length, W=width and h=height
given:
the volume of a box is V=1755ft%5E3
the width of the box is highlight%28W=9ft%29,
and it's height h is 2ft more than it's length L; so, h=L%2B2

to find: the height of the box h
start with V=L%2AW%2Ah...plug in given values

1755=a%2A9%2A%28a%2B2%29
1755=9ft%2A%28a%5E2%2B2a%29
1755=9a%5E2%2B18a
0=9a%5E2%2B18a-1755.......use quadratic formula

L+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

L+=+%28-18%2B-+sqrt%28+18%5E2-4%2A9%2A%28-1755+%29%29%29%2F%282%2A9%29+

L+=+%28-18%2B-+sqrt%28+324%2B63180%29%29%2F18+

L+=+%28-18%2B-+sqrt%28+63504%29%29%2F18+

L+=+%28-18%2B-+252%29%2F18+

L+=+%28-18%2B+252%29%2F18+..we will find only positive solution because the length could be only positive number
L+=+%28-18%2B+252%29%2F18+

L+=+234%2F18

highlight%28L+=+13ft%29
now we can find the height h
h=L%2B2ft
h=13ft%2B2ft
highlight%28h=15ft%29