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):
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:
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.
