Problem 48
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
Verified Answer
The width of the path is 12 feet.
1Step 1: Identify Known Values
Identify the known values from the problem. The length of the pool is 60 feet, the width is 40 feet and the total perimeter of the rectangle formed by the pool and path is 248 feet.
2Step 2: Calculate the Perimeter of the Pool
Let's first calculate the perimeter of the pool using the formula \(2*(length + width)\). Plug the values in to get \(2*(60 + 40) = 200\) feet.
3Step 3: Determining the Perimeter Contributed by the Path
Now, we subtract the perimeter of the pool from the total perimeter to find the additional perimeter contributed by the path. So, \(248 - 200 = 48\) feet.
4Step 4: Find the Width of the Path
The path adds evenly to all sides of the rectangle. Therefore, to find the width of the path, divide the additional perimeter contributed by the path by 4 (since a rectangle has four sides). So the width of the path is \(48 / 4 = 12\) feet.
Other exercises in this chapter
Problem 47
Write each English sentence as an equation in two variables Then graph the equation. The \(y\) -value is four more than twice the \(x\) -value.
View solution Problem 47
Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These a
View solution Problem 48
In Exercises \(45-50,\) perform the indicated operation(s) and write the result in standard form. $$ (4-i)^{2}-(1+2 i)^{2} $$
View solution Problem 48
Solve each equation in Exercises \(47-64\) by completing the square. $$ x^{2}+6 x=-8 $$
View solution