SOLUTION: Find the dimensions of a rectangular box with the width that is 3 times the height and length that is 6 inches more than the height. The volume is 15 cubic inches.
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Question 326163: Find the dimensions of a rectangular box with the width that is 3 times the height and length that is 6 inches more than the height. The volume is 15 cubic inches.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
the height. Then 
represents the width, and 
represents the length. The volume is the product of the three dimensions and is equal to 15 cubic inches, hence:
Take out a 3:
Using the Rational root theorem to determine that the possible rational roots are 
and 
and synthetic division to determine that -1 is, in fact, a root of 
we are left with:
\left(x^2\ +\ 5x\ -\ 5\right)\ =\ 0)
Use the quadratic formula to determine the other two roots. Discard both negative roots since we are looking for a positive measure of length. Once you have determined the height, , you can easily calculate the other two dimensions. Leave everything in radical form for exact answers.
John
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