Question

if the altitudes drawn from vertex of ABC to the opposite sides are equal then prove that triangle is equilateral

Answer 1

hiiii friend
here is your answer
assuming the altitudes be x,y and z for side AB,BC and AC respectively.
so,
I case
area=0.5 × x ×AB

II case
area=0.5 × y ×BC

III case
area=0.5 × z ×AC

as, area must be equal
so,


0.5 × z ×AC=0.5 × y ×BC=0.5 × x ×AB


and also given that x=y=z
therefore
AC=BC=AB


and as the sides are equal then the triangle be equilateral...

hence proved


glad to help you
hope it helps
thank you.