Question

ABC is an isosceles triangle right angled at B. Equilateral triangles are constructed on sides BC and AC. Prove the areas of ΔBCD=1/2ar ΔACE

Answer 1

Answer:

Step-by-step explanation:

In ΔABC,

AC²=BC²+AB²

AC²=2BC²           [As,AB=BC(Isosceles right angle triangle)

InΔACE,

As it is a equilateral triangle it's area=√3/4*a²

ar(ΔACE)=√3/4*AC²

But AC²=2BC²

ar(ΔACE)=√3/4*2BC²=√3/2*BC²

In(ΔBCD),

ar(ΔBCD)=√3/4*BC²

Therefore,ar(ΔACE)/ar(ΔBCD)=1/2

Hence prooved