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?

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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?

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Answer 1 · 2016-10-26T19:09:37

$a = 35x - x^2$

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:

$a = x * (35 - x)$

$a = 35x - x^2$

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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?

1 Answer

Explanation:

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