Question

In a rhombus ABCD, if EA=60° find GB, DC and ID

Answer 1

Step-by-step explanation:

Let each side of the rhombus ABCD be a

∠A=60o

So, ABD is an equilateral triangle

⇒AD=AB=a

We know that, the diagonals of a rhombus bisect each other a right angles

So, in right triangle AOB, we have AO2+OB2=AB2 [By pythagoras Theorem]

AO2=AB2−OB2

=a2−(a1/2)2

=a2−a2/4

3a2/4

AO=√(3a2/4)=√3a/2

But, AC=2AO=2×3a/2=3a

Hence,

AC:BD=√3a:a=√3:1