Problem 26 - Algebra and Trigonometry

Question

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Step-by-Step Solution

Answer

The dimensions of the pool are: width = 40 feet and length = 120 feet.

Step 1: Substitute known relation into perimeter formula

Since it's given that the length of the pool is three times its width, we can substitute \(l = 3w\) into the perimeter formula. The equation becomes \(P = 2(3w) + 2w = 320\), where \(P = 320\) feet is given in the problem.

Step 2: Simplify the equation

The equation in step 1 simplifies to \(6w + 2w = 320\), which further simplifies to \(8w = 320\).

Step 3: Solve for the width

To solve for \(w\), divide both sides of the equation by 8, which gives \(w = 320 / 8 = 40\). Thus, the width of the pool is 40 feet.

Step 4: Calculate the length

As we now know \(w\), we can substitute it into the relation \(l = 3w\) to find the length of the pool. This gives \(l = 3 * 40 = 120\). So, length of the pool is 120 feet.