Question

Yardbird Landscaping has 52 m of fencing with which to enclose a rectangular garden. If the garden is x meters​ long, express the​ garden's area as a function of the length.

Answer 1

f(L)=-L²*26L

Explanation:

Let's start by looking at the formula for a rectangle's perimeter (which is what the fencing implies):
`2L+2W=52`

When the question asks for the garden's area as a function of the length, it's basically saying "whatever value is in the function (as in f(value) ), make that value be the length."

But first we have to find L*W, because that's the function of the area.

1.) Solve for W

`2L+2W=52\\2W=52-2L\\W = 26-L`

2.) Plug in W for the function L*W
`L*(26-L)\\-L^2*26L\\\\Answer: f(L)=-L^2*26L`

Answer 2

Area, A(x) = 26x - x² , as a function of the length (x).

Explanation:

Yardbird Landscaping has 52 m of fencing with which to enclose a rectangular garden.

Let x be the length of garden

So perimeter of rectangle = 52 m

Perimeter = 2 x ( Length + width)

52 = 2 x ( x + width)

Width= 26 - x

`\texttt{Area = Length x Width}\\\\\texttt{Area =}x* (26-x)=26x-x^2\\\\\texttt{Area =}26x-x^2`

Area, A(x) = 26x - x² , as a function of the length (x).