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anonymous
 5 years ago
If K is the area of a triangle ABC and length of its two sides are 3 and 5. if c is the third side then
a)\[K \le (c ^{2}+16c+64)/ 12\sqrt{3}\]
b)\[K = (c ^{2}+16c+64)/ 8\]
c)\[K \ge (c ^{2}+16c+64)/ 4\sqrt{3}\]
d)none of these
anonymous
 5 years ago
If K is the area of a triangle ABC and length of its two sides are 3 and 5. if c is the third side then a)\[K \le (c ^{2}+16c+64)/ 12\sqrt{3}\] b)\[K = (c ^{2}+16c+64)/ 8\] c)\[K \ge (c ^{2}+16c+64)/ 4\sqrt{3}\] d)none of these

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you bring latex in the question?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just formed the equation here.. and pasted it at the question area=)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is it correct? i sort of guessed. See when c=0, obviously K=0 and that cancels b) and c). Now generally according to my experience d)none of these is seldom correct. so a) has a good chance of being correct. ;) Well you may try cosine rule and the sine rule..But getting an inequality given in the question is appearing tough!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0considering c=0 would not make this triangle a triangle right? isnt it kind of risky to thnk like that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if c=0 u don't get a triangle at all, its the degenerated case. so area=K=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why would there be any risk? a,b,c can be reals the question didnt mention POSITIVE reals

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the solution given to the problem is this, [(sa)(sb)(sc)]^1/3 <= 3s(a+b+c)  3 (area^2 /s)^1/3<=s/3 area <= s^2/3rt3=c^2+16c+64/12rt3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but they also said that ABC is a triangle. a triangle has to have three sides

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0one side may be zero..and believe me it works in such questions ;) consider this not as mathematics but just "cheating" the examiner!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well okay..=) can you explain the solution to me buddy?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It was a good question. Use AMGM inequality to (sa),(sb),(sc)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i knw that for two numbers.. but what to do if there are three??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for nnumbers: \[\frac{a+b+c+...n\ terms}{n}\ge \sqrt[n]{abc...}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0numbers need to be NONNEGATIVE REALS

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay got it.. thanx alot!
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