2026 AHS P2 Q9

2026 AHS P2 Q9

Secondary 4
7 marks

The figure \(PQRS\) is formed by triangle \(PQR\) and triangle \(PRS\). Angle \(QRS=90^\circ\), angle \(PRQ=x\), \(RQ=3\text{ cm}\), \(RP=RS=8\text{ cm}\). The area of the figure is \(PQRS\) is \(A\text{ cm}^2\).

  1. Show that \(A=32\cos x+12\sin x\).[2]
  2. Express \(A\) in the form of \(R\cos(x-\alpha)\).[3]
  3. Hence find the maximum value of \(A\) and the corresponding value of \(x\).[2]

Solution:

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Answer:(a) \(A=32\cos x+12\sin x\). (b) \(4\sqrt{73}\cos(x-20.6^\circ)\), with the angle rounded. (c) Maximum \(A=34.2\), at \(x=20.6^\circ\).

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