A rectangular pen is made with 100 m of fencing in three sides. The fourth is a stone wall. Find the greatest possible area of such an enclosure.

Question

anonymous · Answer

P = 100 = 2l + w (since the 4th side is a stone wall)
A = lw

w = 100 - 2l

Substitue into area formula.
$$A=l(100-2l)=100l-2l^{2}$$
So you need to maximise this quadratic.  Maximums and minimums of quadratics occur at the vertex.

Find the vertex and the y-coordinate is the maximum area.