Show that for any triangle with sides `a ,b ,a n dc3(a b+b c+c a)<(a+b+c)^2<4(b c+c a+a b)dot` When are the first two expressions equal ?

In any triangle ABC, the side are a=7,b=5 and c=8. Find A.

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

The number of triplets (a, b, c) of integers such that and a, b, c are sides of triangle with perimeter 21 and a < b < c

The maximum area of the triangle whose sides a,b and c satisfy 0<=a<=1,1<=b<=2 and 2<=c<=3 is

In any triangle,prove that b cos B+c cos C=a cos(B-C)

Let a,b,c denote the lengths of the sides of a triangle such that ( a-b) vecu + ( b-c) vecv + ( c-a) (vecu xx vecv) = vec0 For any two non-collinear vectors vecu and vecu ,then the triangle is

Show that the difference of any two sides of a triangle is less than the third side. Given : A A B C To Prove: (i) A C-A B

Show that the difference of any two sides of a triangle is less than the third side. GIVEN : A A B C TO PROVE : (i) A C-A B

If a,b,c are the sides of triangle then (a)/(c +a -b) + (b)/(a +b -c) + (c )/(b +c-a) can take vlaue (s)