Question

the length of bill's backyard swimming pool is 60 ft longer than the width if the pool. The surface area of the water is 1600 square ft. What is the width of the pool?

Answer 1

Given data:
Surface Area of water = A = 1600
`ft^(2)`
Length of the swimming pool = L = 60
`ft` + W
Width of the swimming pool = W =?

Since,
Area = Length * Width
A = L * W

Therefore,
1600 = (60 + W) * W
1600 = 60W + W*W

=>
`W^(2) + 60W - 1600 = 0`

In the above equation(in terms of quadratic formula),
a = 1
b = 60
c = -1600
x = W

Use,

x(for positive) =
`x =\frac{ -b + \sqrt{ b^(2) - 4*a*c } }{2*a}`
Plug-in the values you would get:
x = (-60 + 100) / 2
x = 20 --- (1)

x(for negative) =
`x =\frac{ -b - \sqrt{ b^(2) - 4*a*c } }{2*a}`
Plug-in the values you would get:
x = (-60 - 100) / 2
x = -80 --- (2)


Since x = W = Width, and width CANNOT be negative, therefore, the correct answer is (1):

Ans: Width = 20ft