Problem 46 - College Algebra Essentials

Question

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Step-by-Step Solution

Answer

The width of the pool is 23 meters and the length is 40 meters.

Step 1: Formulate Equations

Let's denote the width of the pool as \(x\) meters. Since it is given that the length is 6 meters less than twice the width, we can express length as \(2x - 6\) meters. The formula for the perimeter of a rectangle is \(2 * (length + width)\). We are given that the perimeter is 126 meters, so we can substitute the expressions for length and width into the perimeter formula to get: \(2 * (2x - 6 + x) = 126\).

Step 2: Simplify The Equation

Before solve the equation it will be helpful to simplify it. The equation from the previous step we have such as after multiplication \(6x - 12 = 126\). Now we can add 12 to each side of the equation to get \(6x = 138\).

Step 3: Solve For x

To solve for \(x\), we need to isolate \(x\) on one side of the equation. We achieve this by dividing each side of the equation by 6. So, we have \(x = \frac{138}{6} = 23\).

Step 4: Find The Length

Now we can use the value of the width (\(x = 23\)) determine the length. Substituting \(23\) into \(2x - 6\), we get \(2 * 23 - 6 = 46 - 6 = 40\) meters.