the length of bill's backyard swimming pool is 60ft longer than the width of the pool. the surface area of the water is 1600 square feet. what is the width of the pool?
To find the width of the pool, we'll need to set up and solve an equation based on the given information.
Let's assume the width of the pool is represented by 'x' feet. According to the problem, the length of the pool is 60 feet longer than the width. So, the length can be represented as 'x + 60' feet.
To find the area of a rectangle (in this case, the surface area of the pool), we multiply the length and width together. Using the formula for area, we have:
Area = Length × Width
In this case, the surface area of the water is given as 1600 square feet. So, we have:
1600 = (x + 60) × x
Now we can solve this equation to find the value of 'x', which represents the width of the pool.
Let's solve the equation:
1600 = x^2 + 60x
Rearrange the equation to bring all terms to one side:
x^2 + 60x - 1600 = 0
Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 60, and c = -1600.
Plugging these values into the quadratic formula:
x = (-60 ± √(60^2 - 4*1*(-1600))) / (2*1)
Simplifying:
x = (-60 ± √(3600 + 6400)) / 2
x = (-60 ± √10000) / 2
x = (-60 ± 100) / 2
Now we have two possible values for 'x':
x₁ = (-60 + 100) / 2 = 40 / 2 = 20
x₂ = (-60 - 100) / 2 = -160 / 2 = -80
The width of the pool cannot be negative, so we discard the value of -80. Therefore, the width of the pool is 20 feet.
area=LW
L-60=W
1600=(W+60)W multiply it out, and solve for W