Question

A gardener has 200 meter of fencing to enclose two adjacent rectangular plots.What dimensions will produce a maximum enclosed area?

Answer 1

WELCOME TO OPENSTUDY.!!! :D

Answer 2

Now this question is a bit trial and error.
So they say that the gardener has 200m as the perimeter rught?
So
2(Length + Breadth) = 200
So Length + Breadth = 100

Now we cannot measure ALL the possibilities here but
It is is observed that
Length * Breadth = Greatest [Length + Breadth = 100]
48 * 52 = 2496
49 * 51 = 2499
50 * 50 = 2500 [MAXIMUM]

Understood?
I cannot think of a better way! :)

Answer 3

There's always calculus and the first derivative test.

Answer 4

I am not familiar with that.
Maybe you can explain it to him then! :D

Answer 5

Alternatively, there's the AM-GM inequality:
\[\sqrt{LW}\leq\frac{L+W}{2}\]
with equality iff L=W, for all positive L and W.

Answer 6

Thus, \[\sqrt{LW}\leq\frac{100}{2}\Rightarrow\sqrt{LW}\leq50 \Rightarrow LW\leq2500\]
which means LW can only reach up to 2500, if L+W=100, and this happens when L=W=50.