A rectangular swimming pool is 5 feet longer than it is wide. If a concrete walk 2 feet wide is placed around the pool, the area covered by the pool and the walk is 156 square feet greater than the area covered by the pool alone. What are the dimensions of the pool
First, draw a picture to represent the pool with walk around it.
Let x = width of pool, then x + 5 = length of pool
x+ 9 = length of walk, and x+4 = width of walk
Area of pool = x(x +5)
Area of walk and pool =(x + 9)(x + 4)
Area of pool + 156 = Area of walk and pool
x(x + 5) + 156 = (x + 9)(x + 4)
Now, solve the equation for x which wiki give you the width of the pool.
Let's assume that the width of the pool is 'x' feet.
According to the given information, the length of the pool is 5 feet longer than its width, which makes it (x+5) feet.
The area of the pool alone is given by the formula: Area = Length x Width, which is (x+5) x x = x^2 + 5x square feet.
Now, if a concrete walk 2 feet wide is placed around the pool, the total dimensions of the area covered by the pool and the walk will be (x+4) feet longer and (x+4) feet wider than the dimensions of the pool alone.
So the area covered by the pool and the walk is given by the formula: Area = (Length + 2x) x (Width + 2x), which is (x+5+2(2)) x (x+2) = (x+9)(x+2) square feet.
The problem states that the area covered by the pool and the walk is 156 square feet greater than the area covered by the pool alone.
Therefore, we can set up the equation: (x+9)(x+2) - x^2 - 5x = 156.
Now, let's solve this equation step by step:
Expanding the equation:
(x^2 + 11x + 18) - x^2 - 5x = 156
Combining like terms:
6x + 18 = 156
Subtracting 18 from both sides of the equation:
6x = 156 - 18
6x = 138
Dividing both sides of the equation by 6:
x = 138/6
x = 23
So the width of the pool is 23 feet.
Now, we can find the length of the pool by using our initial assumption: Length = Width + 5.
Length = 23 + 5
Length = 28
Therefore, the dimensions of the pool are 23 feet by 28 feet.
To solve this problem, we need to set up equations based on the given information. Let's start by defining the width of the pool as "x" feet.
Since the length of the pool is 5 feet longer than the width, the length of the pool would be "x + 5" feet.
The area of the pool can be calculated by multiplying the length and width: x * (x + 5).
Now, we need to consider the concrete walkway around the pool. The walkway extends 2 feet beyond the pool in all directions. Therefore, the width of the entire area covered by the pool and the walkway would be "x + 4" (2 feet on each side), and the length would be "(x + 5) + 4" (two sides, each adding 5 feet to the pool length).
The area covered by the pool and the walkway is given as 156 square feet greater than the area covered by the pool alone. So, we can set up the equation:
(x + 4) * ((x + 5) + 4) = x * (x + 5) + 156
Expanding the equation, we get:
(x + 4) * (x + 9) = x^2 + 5x + 156
Now, let's simplify this equation:
x^2 + 13x + 36 = x^2 + 5x + 156
Subtracting x^2 from both sides:
13x + 36 = 5x + 156
Next, subtracting 5x from both sides:
8x + 36 = 156
Finally, subtracting 36 from both sides:
8x = 120
Dividing both sides by 8:
x = 15
Therefore, the width of the rectangular swimming pool is 15 feet. Since the length is 5 feet longer, the length of the pool is 15 + 5 = 20 feet.
So, the dimensions of the pool are 15 feet by 20 feet.