This doesn't really have to do with the Web 2.0 Calculator, I just need help.
In these questions in my math book, I am given a length of fence to be used for enclosing the greatest area of land possible. I have to use a quadratic equation to figure out the greatest area. How do I find the equation I am supposed to use, and how does this help me figure out the area?
Here is an example:
An athletic club has 225 feet of fencing to enclose a tennis court. What quadratic function can be used to find the maximum area of the tennis court? Find the maximum area and the lengths of the sides of the resulting fence.
My math book just threw these questions at me without teaching me how to do them.
Let P be the perimeter of the fence = 225
And ..... P = 2 ( Width + Length) .....so.....
225 = 2 (W+ L) divide by 2 in both sides
225 / 2 = W + L subtract W from both sides and simplify
112.5 - W = L (1)
And the area, A, = W * L
A = W * L ..... sub (1) for L
A = W * ( 112.5 - W) simplify
A = 112.5W - W^2 rewrite as
A = -W^2 + 112.5W
We have an "upside down" parabola and is the quadratic we need
The area will be maximized at the W value of -112.5 / [2 * -1] = 56.25
And using (1), the Length will be 112.5 - W = 112.5 - 56.25 = 56.25
So......the maximum area will be (56.25) * (56.25) = 3164.0625 sq ft.
Note that the area is maximized when we have a square with a side of 56.25 ft.....!!!