Question

If all the three altitudes of a triangle are equal the triangle is equilateral.prove it

Answer 1

area of a triangle is 1/2 *(base)(altitude)

which means ares is dependent on only 2 factors base and altitude..

since area of a triangle will always be equal irrespective of which side u take as base..

let base1 has altitude1 as perpendicular and same for rest all..

i can say base1*altitude1 = base2*altitude2 = base3*altitude3 since half is a constant i ignored it

since altitudes are all equal .. bases are bound to be equal if we say area is equal.

hence all sides will be equal making triangle an equilateral triangle..