'The rectangular swimming pool in the figure shown measure 40 feet by 60 feet and is surround by a path of uniform width around the four edges. the perimeter of the rectangular formed by the pool and he surrounding path is 248 feet determine the width of the path'
Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.
To determine the width of the path surrounding the rectangular swimming pool, we need to follow these steps:
1. Let's represent the width of the path as 'x'.
2. The length of the pool with the surrounding path included can be calculated by adding twice the width of the path ('x') to the original length of the pool, which is 60 feet. So the length is represented by the expression 60 + 2x.
3. Similarly, the width of the pool with the surrounding path included can be calculated by adding twice the width of the path ('x') to the original width of the pool, which is 40 feet. So the width is represented by the expression 40 + 2x.
4. The perimeter is the total distance around the shape. In this case, the perimeter is given as 248 feet.
The formula for the perimeter of a rectangular shape is: Perimeter = 2 × (length + width).
Substituting the expressions for length and width, we have:
248 = 2 × (60 + 2x + 40 + 2x)
5. Simplifying the equation, we get:
248 = 2 × (100 + 4x)
6. Distributing the 2:
248 = 200 + 8x
7. Rearranging the equation to isolate 'x':
8x = 248 - 200
8x = 48
8. Solving for 'x' by dividing both sides of the equation by 8:
x = 48 / 8
x = 6
Therefore, the width of the path surrounding the rectangular swimming pool is 6 feet.