Problem 28 - Algebra and Trigonometry

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 dimensions of the pool are: Length = 40 meters, Width = 23 meters.

Step 1: Translate Text to Mathematical Equations

From the first sentence, one can write the algebraic equation L = 2W - 6. From the information about the pool's perimeter, another equation can be written: 2L + 2W = 126.

Step 2: Substitute The First Equation in The Second Equation

To find the values for L and W, one can substitute the first equation into the second: 2(2W-6) + 2W = 126. Simplifying this gives 4W - 12 + 2W = 126, which simplifies even further to 6W - 12 = 126.

Step 3: Solve For W

Next, cancel the -12 from both sides which gives 6W = 138. By then dividing both sides by 6, one can find that W = 23 meters.

Step 4: Solve For L

Substitute W = 23 meters in L = 2W - 6 to get the length L. This gives L = 2*23 - 6 = 40 meters.