Question

In a rhombus abcd, a=60. The ratio of diagonals ac and bd is:

Answer 1

Answer:

I will use the Properties of a rhombus and trigonometry here.

Step-by-step explanation:

As we know about a rhombus, the diagonals of a rhombus bisect each other at 90ⁿ, and the diagonals also bisect the angles formed by the intersection of the adjacent sides.

So, when you are saying that angle A = 60ⁿ,

then you definitely mean that angle AED = 30ⁿ,

And now, let's take a look at ∆AED, which is a right triangle,

Our angle theta = 30°,

then I use the value of Tan 30°,which is equal to 1/√3,

So, Tan(angle EAD) = 1/√3,

SINCE THE TAN IS THE RATIO OF THE SIDES OPPOSITE AND ADJACENT TO THE ANGLE,

THEN ED/AE= 1/√3,

since the diagnolas of a rhombus bisect each other,

then DIAGONAL RATIO= 2* ED/2* AE = ED / AE, which is equal to 1/√3.

So, BD:AC = 1:√3,

THEN, AC:BD = √3:1

NOW, THATS THE CORRECT ANSWER.