A rectangular pen is to be fenced off using exactly 60 m of wire mesh. What is the largest area, in square metres, that can be enclosed?

With $2(l+b)=60$ the two sides must satisfy $l+b=30$, and a product is largest when the two parts of a fixed sum are equal, so $l=b=15$ m and the area = 225 sq m — the square is the best rectangle. The other options are all genuinely possible pens with the same 60 m of wire and smaller areas: $18\times 12=216,20\times 10=200$ and $25\times 5=125$. The further the shape drifts from a square, the less it holds.