SOLUTION: how do you find the dimensions of a rectangle with the smallest perimeter and an area of 120000 inches?

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Question 310895: how do you find the dimensions of a rectangle with the smallest perimeter and an area of 120000 inches?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is,
A=L%2AW=120000
L=120000%2FW
The perimeter of a rectangle is,
P=2%2A%28L%2BW%29
Substituting,
P=2%2A%28120000%2FW%2BW%29
Now P is a function of W only.
To minimize P, find the derivative wrt W and set it equal to zero.
dP%2FdW=2%2A%28-120000%2FW%5E2%2B1%29=0
120000%2FW%5E2=1
W%5E2=120000
W=sqrt%28120000%29
From the area equation above,
L=120000%2FW=120000%2Fsqrt%28120000%29=sqrt%28120000%29
The rectangle with the smallest perimeter and area of 120000 sq. in. is a square with sides of sqrt%28120000%29 in.