Question

Bob wants to fence in a rectangular garden in his yard. He has 70 feet of fencing to work with and wants to use it all. If the garden is to be x feet wide, how do you express the area of the garden as a function of x?

Answer 1

`a = 35x - x^2`

Explanation:

Having `70`ft of fencing with a `w`idth of `x` feet and knowing the perimeter of a rectangle is `p = 2w + 2l` we can state the length of the garden as:

`70 = 2x + 2l` and solving for `l` we know the length with be:

`2l = 70 - 2x`
or
`l = 35 - x`

And then knowing the formula for the area of a rectangle is `a = w * l` we can write the equation as:

`a = x * (35 - x)`

`a = 35x - x^2`