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If Delta is the area of a triangle with...

If `Delta` is the area of a triangle with side lengths ` a, b, c,` then show that as `Delta leq 1/4 sqrt((a + b + c) abc)` Also, show that the equality occurs in the above inequality if and only if `a = b = c`.

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ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
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  2. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

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  3. Prove that : (r1)/(b c)+(r2)/(c a)+(r3)/(a b)=1/r-1/(2R)

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  4. Prove that : (tanA/2)/((a-b)(a-c))+(tanB/2)/((b-a)(b-c))+(tanC/2)/((c-...

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  5. Prove that in a triangle (b c)/(r1)+(c a)/(r2)+(a b)/(r3)=2R\ [(a/b+b...

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  6. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

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  7. In a scalene triangle ABC the altitudes AD & CF are dropped from the v...

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  8. Let a, b, c be the sides of a triangle & Delta its area. Prove that a^...

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  9. If in a triangle of base 'a', the ratio of the other two sides is r ( ...

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  10. If Delta is the area of a triangle with side lengths a, b, c, then s...

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  11. Which of the following pieces of data does NOT uniquely determine an ...

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  12. If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3...

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  13. If a ,b ,c denote the lengths of the sides of a triangle opposite t...

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  14. One angle of an isosceles triangle is 120^0 and the radius of its incr...

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  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

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  16. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

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  18. Let P Q R be a triangle of area with a=2,b=7/2,a n dc=5/2, w h e r ea...

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  19. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

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  20. In a triangle the sum of two sides is x and the product of the same is...

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