If the area of \DeltaPQR above is 12\(\sqrt{3}\) cm\(^2\), find the value of q?
Attached Figure / Diagram
A
6 cm
B
7 cm
C
8 cm
D
5 cm
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Area of a triangle = \(\frac{1}{2}\) ab Sin\theta
12\(\sqrt{3}\) = \(\frac{1}{2}\) x 8 x q sin 60
12\(\sqrt{3}\) = 4 x q x \(\frac{\sqrt{3}}{2}\)
12\(\sqrt{3}\) = 2q\(\sqrt{3}\)
q = \(\frac{12\sqrt{3}}{2\sqrt{3}}\)
q = 6cm.
Source: Myschool Past Questions Archive (Record #9958)