If the area of △ △ PQR above is 12√3 3 cm2, find the value of q?

If the area of $△$PQR above is 12$\sqrt{3}$cm2, find the value of q?

Answer Details

Let A denote the area of $△$PQR, then A = $\frac{1}{2}bh$

Using Sin 60${}^{\circ }$ = $\frac{h}{q}$

h = q sin 60${}^{\circ }$

So A = $\frac{1}{2}b\left(q\sin {60}^o\right)$

12$\sqrt{3}=\frac{1}{2}\times 8\times q\times \frac{\sqrt{3}}{3}$

12$\sqrt{3}$ - 2q$\sqrt{3}$

q = $\frac{12}{2}=6$cm