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Chapter 0: Problem 28

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?

Short Answer

Expert verified
The width of the pool is 21 meters and the length is 36 meters.

Step by step solution

01

Formulate the Equations

Start by converting the given problem into algebraic form. Let's denote the width of the rectangular pool as \(w\). According to the problem, the length of the pool is 6 meters less than twice the width. This can be expressed as \(l = 2w - 6\). The formula to calculate the perimeter of a rectangle is \(P = 2l + 2w\). Substituting the given perimeter (126m), we get \(126 = 2l + 2w\) as our second equation.
02

Substitute and Solve

We can substitute the 1st equation (\(l = 2w - 6\)) into the 2nd equation (\(126 = 2l + 2w\)), replacing the \(l\) in the 2nd equation. It becomes: \(126 = 2(2w - 6) + 2w\). Now simplifying this equation will give us the value of \(w\), the width of the pool.
03

Solve for Length

Once we have the width (\(w\)), we can substitute it into the first equation (\(l = 2w - 6\)) to get the length (\(l\)) of the pool.
04

Validate the Solution

After finding the dimensions of the pool, one needs to verify them by substituting these dimensions in the perimeter equation \(P = 2l + 2w\). The result should equate to the given perimeter in the problem (126m). If it doesn't, then an error occurred during the calculations and needs to be rectified.

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