If `Delta` denotes the area of any triangle and s its semiperimeter, prove that `Delta` is less than S^2/4`

If Δ denote the area of any triangle with semi-perimeter , then

The sides of a triangle are in A.P. and its area is 3/5t h of the an equilateral triangle of the same perimeter, prove that its sides are in the ratio 3:5:7, and find the greatest angle of the triangle.

In a right angles triangle, prove that r+2R=s.

Prove that the area of a triangle is invariant under the translation of the axes.

If triangle is the area and 2s is the perimeter of triangleABC , then prove that triangle le s^(2)/(3sqrt(3))

In any triangle A B C , prove that: Delta=(b^2+c^2-a^2)/(4cotA) .

Let Delta denote the area of the DeltaABCand Delta p be the area of its pedal triangle. If Delta=k Deltap, then k is equal to

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Prove that the perimeter of a triangle is greater than the sum of its three medians.