Question

A rectangle is twice as long as it is wide. Express the area of the rectangle as a function of its perimeter P.

Answer 1

Add all of the sides up

Answer 2

SO p = 6w

Answer 3

p(w) = 6w

Answer 4

A = 1/3p^2

Answer 5

Can i ask how you got there DocLav?

Answer 6

Okay so the area would be length x width which would be 2w^2 right.

Answer 7

Yes.

Answer 8

So you want to derive the 2w^2 from the perimeter or 6w

Answer 9

You have to square it to get the square. To get 2 you divide 6 by 1/3.

Answer 10

So did you set 6w= 2w^2 and go from there?

Answer 11

Sort of but it is more trying to manipulate the equation.

Answer 12

What about the p in your equation? How did you get that into the answer for area?

Answer 13

The p = 6w

Answer 14

So what is the first equation you set up after you get the 6w and the 2w^2

Answer 15

\[\text{Area}=\frac{P^2}{18} \]\[p=6w \]\[p^2=36w^2 \]\[\frac{p^2}{18}=\frac{36w^2}{18} \]\[\frac{p^2}{18}=2 w^2=\text{Area} \]