Question

Find a formula for the described function.
A rectangle has perimeter 12 m. Express the area A of the rectangle as a function of the length, L, of one of its sides.

Answer 1

Answer:

$A= 6L -L^2$

Step-by-step explanation:

Let's define some notation first:

L = represent the length for the rectangle

A = represent the area for the rectangle

W= represent the width for the rectangle

From the info given we know that P= 12m

And the perimeter for a rectangle is given by:

$P=2L+ 2W=12$

From this equation we can solve for W like this:

$2W= 12-2L$

$W= 6 -L$

Now we can use the formula for the area of a rectangle given by:

$A= L*W$

And if we replace the expression founded for W, we got:

$A= L* (6-L)$

$A= 6L -L^2$

And that would be our final answr in terms of the length.