The diagram shows a figure $PQRST$ which consists of a rectangle $PQST$ and an isosceles triangl

Question

The diagram shows a figure $PQRST$ which consists of a rectangle $PQST$ and an isosceles triangle $QRS$. It is given that $PQ = 4$ cm and $QR = 8$ cm. Given angle $SQR =$ angle $QSR = x$ radians and the area of $PQRST$ is given by $A$ $\text{cm}^2$, show that $A = 64\cos x + 32\sin 2x$.[4] Find the value of $x$ for which $A$ has a stationary value.[3] Hence find the exact stationary value of $A$ and determine whether it is a maximum or a minimum.[2]

Accepted Answer

(b) $x = \frac{\pi}{6}$ (c) $A = 48\sqrt{3}$ cm$^2$; Maximum

2024 CGSS P2 Q6

2024 CGSS P2 Q6