Question

suppose you have 102m of fencing to make two side by side rectangles, making one large rectangle when put together. What is the maxium area that you can enclose?

Answer 1

I assume you wont have a double side on the adjoining sides.


If you do this, you have 102 m of perimeter, to do 3 widths (two ends and center fence), and 2 lengths.

Area= lw

P= 3w+2L or L= 1/2(102-3w)
Area= 1/2 w(102-3w)

This is easy in calc, but I assume you are not there yet. So graph it, notice the max Area, read w. Then solve for l.

In Calculus, the maximum Area occurs when dArea/dw=0

dArea/dw=0=1/2 (102-3w) + 1/2w(-3) solve for w.

Answer 2

Thank you so much for the help