SOLUTION: What is the minimum perimeter possible for a rectangle with an area or 500cm squared

Algebra ->  Points-lines-and-rays -> SOLUTION: What is the minimum perimeter possible for a rectangle with an area or 500cm squared      Log On


   

Question 310541: What is the minimum perimeter possible for a rectangle with an area or 500cm squared
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter of a rectangle
P=2%2A%28L%2BW%29
Area of a rectangle
A=L%2AW=500
L=500%2FW
Substitute this expression into the perimeter equation,
P=2*(500/W+W)
Now perimeter is a function only of W.
To find the minimum, take the derivative wrt W and set it equal to zero.
P=1000%2FW%2B2W=1000W%5E%28-1%29%2B2W
dP%2FdW=-1000W%5E%28-2%29%2B2=2-1000%2FW%5E2=0
1000%2FW%5E2=2
W%5E2=500
W=sqrt%28500%29
Since L%2AW=500, then
L=sqrt%28500%29
The shape that minimizes perimeter is a square of side sqrt%28500%29.
Pmin=4sqrt%28500%29