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?
w(w+60) = 1600
now crank it out.
hint: 20*80=1600
To find the width of the pool, we can set up an equation based on the given information:
Let's assume the width of the pool is "x" feet.
According to the problem, the length of the pool is 60 feet longer than the width. So, the length would be "x + 60" feet.
The surface area of a rectangle can be calculated by multiplying the length by the width. In this case, the surface area is given as 1600 square feet.
So, we have the equation:
Length * Width = Surface Area
(x + 60) * x = 1600
To solve this equation, we can simplify it by distributing x to each term inside the brackets:
x^2 + 60x = 1600
Rearranging the equation to standard quadratic form:
x^2 + 60x - 1600 = 0
Now, we can solve this quadratic equation to find the value of "x" (width of the pool).
We can factorize the quadratic equation:
(x - 20)(x + 80) = 0
Setting each factor to zero:
x - 20 = 0 or x + 80 = 0
Solving these equations, we get:
x = 20 or x = -80
Since the width cannot be negative, we discard x = -80 as an extraneous solution.
Therefore, the width of the pool (x) is 20 feet.