Trigonometric Equations Question 330
Question: Area of the triangle is $ 10\sqrt{3} $ sq. cm, angle $ C=60^{o} $ and its perimeter is 20 cm, then side c will be
Options:
A) 5
B) 7
C) 8
D) 10
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \Delta =10\sqrt{3} $ $ \Delta =\frac{1}{2}ab\sin C\Rightarrow ab=20\sqrt{3}\frac{2}{\sqrt{3}}=40 $ ?.. (i) Also $ a+b+c=20 $ or $ a+b=(20-c) $ Now, $ \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}=\frac{1}{2} $
Þ $ a^{2}+b^{2}-c^{2}=ab $
Þ $ {{(a+b)}^{2}}-c^{2}=ab+2ab=3ab $
Þ $ {{(20-c)}^{2}}-c^{2}=3(40) $
Þ $ -40c+400=120\Rightarrow c=7 $ .
BETA
