Problem 30 - Algebra and Trigonometry

Question

The rectangular swimming pool in the figure shown measures 40 feet by 60 feet and is surrounded by a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 248 feet. Determine the width of the path.

Step-by-Step Solution

Answer

The width of the path is 6 feet.

Step 1: Understand the problem and draw a diagram

Draw a diagram of the rectangular pool with the walkway around it. The pool dimensions are 40 feet by 60 feet. The path width is uniform and unknown, let's represent it as 'x'.

Step 2: Set up the perimeter equation

Write the formula for the perimeter of a rectangle, which is 2*(length + width). In this case, the length and width are increased by the width of the path (2x). So, the new length will be (60+2x) feet and the new width will be (40+2x) feet. This gives the equation 2*((60+2x) + (40+2x)) = 248.

Step 3: Simplify the equation

Rewrite the equation after simplification: 200 + 8x =248.

Step 4: Solve the equation for x

Subtract 200 from both sides to isolate the term with x. This gives 8x = 48. Finally, divide both sides by 8 to solve for x.