Question

if one of the diagonal of a rhombus is equal to side of the Rhombus prove that it's diagonals are in the ratio √3:1 to each other

Answer 1

We know that diagonals of rhombus

bisect each other at 90°

Let the side of the rhombus be 2a unit.

So,one of its diagonals is also 2a unit

Let other diagonal be 2x unit .

So,when diagonals bisect each other

It will be right angle∆.and side

containing right∆will be a and x unit .

So,by Pythagoras theorem

(2a)^2=(a)^2+(x)^2

=>4a^2-a^2=x^2

=>3a^2=x^2

=>x=√3a

So, diagonals are 2x and 2a

I.e 2√3a and 2a

So,ratio=2√3:2=√3:1

Hence,proved

Hope it helps