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<p>A gardener designs a flower bed \(ABCDE\) in the shape of a rectangle with an equilateral triangle on one of the shorter sides. Side \(AE\) is of length \(a\text{ m}\) and side \(ED\) is of length \(b\text{ m}\) <strong>(see diagram)</strong>. The total perimeter of the flower bed is \(20\text{ m}\).</p>
<p>Find the maximum possible area of the flower bed, showing that it is a maximum value. Give your answer correct to \(4\) significant figures.<span class="inline-marks">[6]</span></p>

A gardener designs a flower bed \(ABCDE\) in the shape of a rectangle with an equilateral triangle on one of the shorter sides. Side \(AE\) is of length \(a\text{ m}\) and side \(ED\) is of length \(b\text{ m}\) **(see diagram)**. The total perimeter of the flower bed is \(20\text{ m}\).

Find the maximum possible area of the flower bed, showing that it is a maximum value. Give your answer correct to \(4\) significant figures.

N2024 P2 Q2

N2024 P2 Q2