The diagram shows a triangle $PQR$. Point $M$ lies on $QR$ such that $QM = 1$ unit and

Question

The diagram shows a triangle $PQR$. Point $M$ lies on $QR$ such that $QM = 1$ unit and $MR = 3$ units. $\angle PRQ = 90{}^\circ$ and $PR$ is $x$ units. Angles $QPR$ and $MPR$ are denoted by $\alpha$ and $\beta$ respectively as shown, where $0{}^\circ < \alpha < 45{}^\circ$. Given $\tan(\alpha - \beta) = \frac{1}{8}$, find the value of $x$.[5]

Accepted Answer

x = 6

2025 CGSS PRELIMS P1 Q9

2025 CGSS PRELIMS P1 Q9