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?

Oct 26, 2016

$a = 35 x - {x}^{2}$

Explanation:

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

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

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

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

$a = x \cdot \left(35 - x\right)$

$a = 35 x - {x}^{2}$