Applications Of Derivatives Question 308
Question: Of the given perimeter, the triangle having maximum area is
Options:
A) Isosceles triangle
B) Right angled triangle
C) Equilateral
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
First we observe that triangle ABC having base AB, the area of $ \Delta ABC $ is greatest for which the altitude of C w.r.t. AB is greatest.
Let $ \theta $ be the semi-vertical angle of such a triangle ABC. $ S= $ area of the $ t=2 $
$ =2\frac{a^{2}}{2}\sin (\pi -2\theta )+\frac{1}{2}a^{2}\sin 4\theta $
$ =a^{2}\sin 2\theta +\frac{a^{2}}{2}\sin 4\theta $ Now S is maximum when $ \theta =\frac{\pi }{6} $ or $ 2\theta =\frac{\pi }{3} $ i.e., triangle is equilateral.
BETA
