
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

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...

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.

: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
