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