Trigonometric Equations Question 46
Question: The sides of triangle are $ 3x+4y,\ 4x+3y $ and $ 5x+5y $ units, where $ x,\ y>0. $ The triangle is
[AIEEE 2002]
Options:
A) Right angled
B) Equilateral
C) Obtuse angled
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Let $ a=3x+4y,,b=4x+3y $ and $ c=5x+5y $ . Clearly, c is the largest side and thus the largest angle C is given by $ \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}=\frac{-2xy}{2,(12x^{2}+25xy+12y^{2})}<0 $
$ \Rightarrow $ $ C $ is an obtuse angle. Trick: Check by putting $ x=1, $ $ y=1 $ .
BETA
