SOLUTION: A carpenter is building a rectangle room with a fixed perimeter of 356 ft. What dimensions would yield the maximum area? What is the maximum area?

Question 329416: A carpenter is building a rectangle room with a fixed perimeter of 356 ft. What dimensions would yield the maximum area?
What is the maximum area?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
THe perimeter of a rectangle is,

The area of a rectangle is,

From the perimeter equation,

Substitute into the area equation,

Now the area is a function of one variable.
To find the maximum, take the derivative wrt W and set it equal to zero.

Then from above,

The maximum area for a given perimeter is obtained using a square.
sq.ft.
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