document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #441004 by jsmallt9(3758) $\"\"$ $\"About$

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For a box (right rectangular prism, in Mathematical terms), the volume is found using: V = l*w*h (length times width times height).

\n" ); document.write( "We've been given that the volume is $\"120m%5E3\"$ . We know the width, 4m. Let's call the length \"x\". Then, since the height is 1m less, the height would be x-1.

\n" ); document.write( "Substituting these numbers and expressions into the volume formula we get:
\n" ); document.write( " $\"%28120%29+=+%28x%29%2A%284%29%2A%28x-1%29\"$
\n" ); document.write( "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 $\"120+=+x%2A4%2Ax-1\"$ we would have the wrong equation!

\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"120+=+%284x%29%2A%28x-1%29\"$
\n" ); document.write( "Using the Distributive Property:
\n" ); document.write( " $\"120+=+4x%5E2-4x\"$

\n" ); document.write( "Now we solve for x. This is a quadratic equation so we want one side to be zero. Subtracting 120 from each side:
\n" ); document.write( " $\"0+=+4x%5E2-4x-120\"$
\n" ); document.write( "Factor. First the GCF:
\n" ); document.write( " $\"0+=+4%28x%5E2-x-30%29\"$
\n" ); document.write( "Then the trinomial:
\n" ); document.write( " $\"0+=+4%28x-6%29%28x%2B5%29\"$
\n" ); document.write( "Zero Product Property:
\n" ); document.write( "4 = 0 or x-6 = 0 or x+6 = 0
\n" ); document.write( "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:
\n" ); document.write( "x = 6 or x = -6

\n" ); document.write( "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. \n" ); document.write( "

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