Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-6 Complete the Square - Practice and Problem-Solving Exercises: 18

Answer

The dimensions are $6\times12\times30$

Work Step by Step

We know that the side lengths are $6, x,$ and $2.5x$. The formula for the volume of a rectangular prism is $lwh$. So, our equation is $6\times x\times2.5x=2160$, which equals $15x^2=2160$. Then, we divide both sides by 15 to isolate $x^2$ to get $x^2=144$. Take the square root of both sides to get $x=\pm12$. The answer is 12 because the length of a pool can't be negative. Now, we substitute 12 into $x$ and $2.5x$, which were the dimensions that we determined in the beginning. $x=12$ $2.5(12)=30$
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