1. ## Perimeter help?

Hello!
I am trying to figure out this problem

A field is to be marked off in the shape of a rectangle of area 144 square feet.

a. Write an expression for the perimeter, P, as a function of the length x

for this, so far i know that the perimeter is 2l + 2w so how would i set this up?

b. Use a calculator to approximate the dimensions for which the perimeter is a minimum ( I don't understand what this means)

thanks for helping! ;D

2. For a) you are asked to set up a set of simultaneous equations so that you get a function in terms of JUST the length...

If $\displaystyle x$ is the length and $\displaystyle y$ is the width, then

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

Since $\displaystyle A = 144\,\textrm{ft}^2$, that means

$\displaystyle 144 = xy$

$\displaystyle y = \frac{144}{x}$.

So $\displaystyle P = 2x + 2\left(\frac{144}{x}\right)$

$\displaystyle P = 2x + \frac{288}{x}$.

b) I suppose you are asked to generate a list which gives you the perimeter for a number of $\displaystyle x$ values. Otherwise you would be expected to use Calculus...

3. You know that P = 2L + 2W, right?

The exercise asks you to express P as a function of the lenght L. You know that the area of the rectangle is 144, therefore W.L = 144. If you put W = 144/L, you can express P as P = 2L + 288/L.

Next, use your calculator to play with the function. Try some numbers and see if you can find one L that minimizes the value of P. I suggest you make a table with the values of L and the correspondent value of P.

4. :O inteseresting! thank you!
and for b) this is for my AP calc summer assignment... what would i need from calc to solve it? :S

5. thank you so much!!