A rectangular swimming pool is 7 meters longer then it is wide. It is surrounded by a concrete walkway 1.5 meters wide. The area of the walkway is 120 meters squared. What are the dimensions of the pool?
width of pool ---> x
length of pool --> x+7
area of pool = x(x+7)
width of whole pool area = x+3
length of whole pool area = x+7+3 = x+10
area of pool area = (x+3)(x+10)
area of concrete walkway = area of whole thing - area of pool
solve
120 = (x+3)(x+10) - x(x+7)
etc.
(you should get x = 15)
To find the dimensions of the pool, we can solve this problem step by step.
Let's assume the width of the swimming pool is "w" meters.
According to the problem, the length of the pool is 7 meters longer than the width, so the length will be "w + 7" meters.
To find the area of the walkway, we can subtract the area of the pool from the area of the pool and the walkway combined.
The area of the pool and the walkway combined is equal to the area of the pool plus two times the product of the pool's width and the walkway's width. So, we can write the equation as follows:
Area of the pool + 2(w + 7)(1.5) = Area of the pool + 120
Now let's solve this equation step by step:
First, we distribute 2(w + 7) to 1.5:
Area of the pool + 3(w + 7) = Area of the pool + 120
Next, simplify the equation:
Area of the pool + 3w + 21 = Area of the pool + 120
We can eliminate the "Area of the pool" terms on both sides of the equation:
3w + 21 = 120
Now subtract 21 from both sides of the equation:
3w = 99
Divide both sides of the equation by 3 to isolate "w":
w = 33
Therefore, the width of the pool is 33 meters.
Now, we can substitute this value of "w" into the length equation to find the length of the pool:
Length = Width + 7 = 33 + 7 = 40 meters.
So, the dimensions of the pool are 33 meters by 40 meters.