A rectangular swimming pool is $6$ ft. deep. One side of the pool is $2.5$ times longer than the other side. The amount of water needed to fill the pool is $2160$ cubic feet. Find the dimensions.
Do you set it up like the following?$$2.5x^2 = 2160$$
The answer I got is: \begin{align*} 2.5x & = 73.5\\ x & = 29.4 \end{align*}
Is that correct?
Let $x$ be the shorter side of the pool (the width). Then the longer side of the pool is $2.5x$. Thus the volume of water in the pool is $(6)(x)(2.5x)$. Set this equal to $2160$ and solve for $x$.
Our equation simplifies to $15x^2=2160$, and then nicely to $x^2=144$.
Thus the pool has width $12$ feet and length $30$ feet.