# Thread: 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.

I think the answer is

p = 2(2 + x)

Can someone please verify?

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.

I think the answer is

p = 2(2 + x)

Can someone please verify?
Let the length of the rectangle be $\displaystyle x$ and the width be $\displaystyle y$.

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

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

$\displaystyle 4 = xy$

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

Therefore

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

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

So no, your answer is not correct.

3. Thanks for the correction. I just picked up a book and this problem was one of first exercises. The old solve equations with a few unknowns eluded me. Thank you kindly for the verification.