of a rectangle that has the given perimeter and a maximum area.

Perimeter : 80 meters

Im still not sure how to set these up to prove with calculus.

2x+2y=80?

Printable View

- October 25th 2009, 06:47 PMNightasylumFind length and width
of a rectangle that has the given perimeter and a maximum area.

Perimeter : 80 meters

Im still not sure how to set these up to prove with calculus.

2x+2y=80? - October 25th 2009, 06:52 PMChris L T521
Let a rectangle have length and width .

Then by the first condition, we have .

Let . It follows from above that .

Substituting this into the area equation, we have .

Since we want to maximize area, it follows that . Now, we find the critical point:

(To verify its a max, we differentiate again to get )

Since , it follows that .

Therefore, the dimensions of the rectangle that gives us the maximum area actually form a square.

Does this make sense? - October 25th 2009, 06:57 PMNightasylum