Question 718556: The volume of a box is 120m3. If the width of the box is 4m,and the height is 1m less than the length, find the height of the box
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! For a box (right rectangular prism, in Mathematical terms), the volume is found using: V = l*w*h (length times width times height).
We've been given that the volume is  . We know the width, 4m. Let's call the length "x". Then, since the height is 1m less, the height would be x-1.
Substituting these numbers and expressions into the volume formula we get:
Note the use of parentheses. It is a very good habit to use parentheses like this when making substitutions. Sometimes they are not necessary but sometimes they are critical. The parentheses around the 120, the x and the 4 are not necessary (but they don't hurt anything, either). The parentheses around x-1 are critical!! If we wrote  we would have the wrong equation!
Simplifying...
Using the Distributive Property:
Now we solve for x. This is a quadratic equation so we want one side to be zero. Subtracting 120 from each side:
Factor. First the GCF:
Then the trinomial:
Zero Product Property:
4 = 0 or x-6 = 0 or x+6 = 0
Solve these. The first equation is simply false. There are no solutions (numbers that make it true) for it. Solving the other two we get:
x = 6 or x = -6
Since x represents the length of the box and since negative lengths make no sense, we reject the negative solution. So the only solution is x = 6. In words, the length is 6m. And since the height is x-1, the height is 5.
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