A rectangular swimming pool measures 15 meters by 10 meters. How wide must a concrete walk around the pool be if the walk is to cover an area of 116 square meters
To find the width of the concrete walk around the pool, we can subtract the area of the pool from the total area including the walk.
1. Calculate the area of the pool.
- Area = length * width
- Area of the pool = 15 meters * 10 meters = 150 square meters
2. Calculate the total area with the walk included.
- Total area = area of the pool + area of the walk
- Total area = 150 square meters + 116 square meters = 266 square meters
3. Subtract the area of the pool from the total area to find the area of the walk.
- Area of the walk = Total area - Area of the pool
- Area of the walk = 266 square meters - 150 square meters = 116 square meters
4. Determine the width of the concrete walk.
- Width = Area of the walk / length or width of the pool
- Width = 116 square meters / 15 meters or 10 meters (choose either length or width)
- Width = 7.73 meters (rounded to two decimal places)
Therefore, the concrete walk around the pool must be approximately 7.73 meters wide.
To find the width of the concrete walk around the pool, we need to subtract the area of the pool from the total area covered by the pool and the walk.
The area of the pool is given by the length multiplied by the width:
Area of the pool = Length * Width = 15 meters * 10 meters = 150 square meters
To find the total area covered by the pool and the walk, we add the area of the pool to the area of the walk:
Total area = Area of the pool + Area of the walk = 150 square meters + 116 square meters
To find the width of the walk, we set up an equation:
Total area = (Length + 2 * Width) * (Width + 2 * Width)
266 = (15 + 2W) * (10 + 2W)
Expanding the equation:
266 = 150 + 30W + 4W^2
Rearranging the equation:
4W^2 + 30W + 150 - 266 = 0
4W^2 + 30W - 116 = 0
Now, we can solve this quadratic equation to find the value of W using factoring, completing the square, or the quadratic formula. In this case, let's use factoring:
Factoring the equation:
(2W + 14)(2W - 8) = 0
Setting each factor equal to zero:
2W + 14 = 0 or 2W - 8 = 0
Solving for W:
2W = -14 or 2W = 8
W = -14/2 or W = 8/2
W = -7 or W = 4
Since the width cannot be negative, we discard W = -7 and take W = 4 as the width of the concrete walk around the pool.
Therefore, the concrete walk must be 4 meters wide.
subtract the pool from the total to get the area of the walk:
(15+2w)(10+2w) - 15*10 = 116
now just solve for w