Question

if two Triangles have equal area and one side of One triangle is equal to one side of the Other triangle then prove that their corresponding altitude saree equal

Answer 1

Given : we know that area of (ABC ) = area of (DEF) ,BC=DF is also given
To prove :AL = DM
Proof : it is given that area of both triangles are equal so ,
ar(ABC)=ar(DEF)
we area of triangle is 1/2 . base . height so,
area of triangle ABC = 1/2 . BC . AL (let it be equation 1)
similarly area of triangle DEF =1/2 . DE . DM (let it be equation 2)
now we know both triangle are same in area so we can consider both equation to be equal
therefor 1/2 . BC . AN = 1/2 . DE . DM
so we get ,
altitude AL = altitude DM
hence proved .

Answer 2

Ok so there are 2 methods to prove this:
1. By construction
2. Easier one by formula
so, you have to just keep their areas
equal and then substitute the equal side in one of the equation. Now using similarities in triangles you can easily price that.