2024 FMSS PRELIMS P1 Q5
2024 FMSS PRELIMS P1 Q5
7 marks
The diagram shows a shape made by cutting an equilateral triangle out of a rectangle of width \(x\) cm.
The perimeter of the shape is \(20\) cm.
- Show that the area, \(A\) \(\text{cm}^2\), of the shape is given by \(A = 10x - \left(\frac{6 + \sqrt{3}}{4}\right)x^2\).[3]
- Given that \(x\) can vary, find the value of \(x\) which produces the maximum area and calculate this maximum area. Give your answers to \(2\) significant figures.[4]
Solution:
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Answer:(i) \(A=10x-\dfrac{6+\sqrt3}{4}x^2\) (shown) (ii) \(x=2.6\), maximum area \(13\text{ cm}^2\) (both \(2\) s.f.).
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