# Math Help - perimeter / area verification problem

1. ## perimeter / area verification problem

A rectangle is required to have an area of 4 square feet but it's dimensions may vary. If one side has a length x, express the perimeter p of the rectangle as a function of x.

p = 2(2 + x)

2. Originally Posted by squidly
A rectangle is required to have an area of 4 square feet but it's dimensions may vary. If one side has a length x, express the perimeter p of the rectangle as a function of x.

p = 2(2 + x)

Let the length of the rectangle be $x$ and the width be $y$.

So $A = xy$ and $P = 2x + 2y$.

You're also told $A = 4$, so

$4 = xy$

$y = \frac{4}{x}$.

Therefore

$P = 2x + 2\left(\frac{4}{x}\right)$

$P = 2x + \frac{8}{x}$.