Question

If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio 

(a) √3 :1 

(b) √2 :1 

(c) 3 : 1 

(d) 2 : 1

Answer 1

(a)   \(\sqrt3\) : 1

Let side AB = diagonal AC = a units 

Then, the other diagonal

= 2 x \(\sqrt{a^2-(\frac{a}{2})^2}\)

= 2 x \(\sqrt{a^2-\frac{a^2}{4}}\)

= 2 x \(\sqrt{\frac{3a^2}{4}}\) = \(\sqrt3\) a

∴ Required ratio = \(\frac{\sqrt3a}{a}\) = \(\sqrt3\) : 1.