JAMB Mathematics 2010 Paper

Concept:To find side $q$ of $\Delta PQR$, use the formula for the area of a triangle when two sides and the included angle are known.Explanation:The area of a triangle is given by $\text{Area} = \frac{1}{2}ab\sin\theta$.From the diagram, the two sides forming the included angle are $8$ cm and $q$ cm, and the included angle is $\theta = 60^\circ$.Given that the area is $12\sqrt{3}$ cm$^2$, substitute into the formula:$$12\sqrt{3} = \frac{1}{2} \times 8 \times q \times \sin 60^\circ.$$Since $\sin 60^\circ = \frac{\sqrt{3}}{2}$, the equation becomes:$$12\sqrt{3} = 4q \times \frac{\sqrt{3}}{2}.$$Simplify:$$12\sqrt{3} = 2q\sqrt{3}.$$Divide both sides by $2\sqrt{3}$:$$q = \frac{12\sqrt{3}}{2\sqrt{3}} = 6.$$Therefore, the length of side $q$ is $6$ cm.Answer:$q = 6$ cm Option A.