SOLUTION: A rectangle has an area of 7056 meters squared. Find the minimum perimeter of the rectangle. Show ALL work to recieve FULL credit.

Algebra ->  Rectangles -> SOLUTION: A rectangle has an area of 7056 meters squared. Find the minimum perimeter of the rectangle. Show ALL work to recieve FULL credit.      Log On


   



Question 1030924: A rectangle has an area of 7056 meters squared. Find the minimum perimeter of the rectangle. Show ALL work to recieve FULL credit.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=L%2AW=7056
P=2L%2B2W=2%28L%2BW%29
From above,
L=7056%2FW
Substituting,
P=2%287056%2FW%2BW%29
To minimize, take the derivative with respect to W.
dP%2FdW=2%28-7056%2FW%5E2%2B1%29
Set it equal to zero,
-7056%2FW%5E2%2B1=0
7056%2FW%5E2=1
W%5E2=7056
W=84
So then,
L=7056%2F84
L=84
So,
P%5Bmin%5D=2%2884%2B84%29
P%5Bmin%5D=2%28168%29
P%5Bmin%5D=336m