Pete has $180$ cm of wire. He bends it to form the outline of his brand logo, which consists

Question

Pete has $180$ cm of wire. He bends it to form the outline of his brand logo, which consists of a semicircle centered on top of a rectangle as shown in the diagram below. The width and length of the rectangle are $3a$ cm and $b$ cm respectively. The diameter of the semicircle is one-third the width of the rectangle. Find the maximum possible area enclosed by the wire, showing that it is a maximum value. Give your answer correct to $2$ decimal places.[6]

Accepted Answer

The maximum enclosed area is $1925.82\text{ cm}^2$ (2 d.p.).

2025 EJC P1 Q2

2025 EJC P1 Q2

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