Question

The diagonals of a rhombus are $12cmand24cm$. The radius of the circle inscribed in the rhombus, is

• A. $\frac{12}{\sqrt{5}}cm$
• B. $\frac{6}{\sqrt{5}}cm$
• C. $6\sqrt{5}cm$
• D. Not possible as a circle in a rhombus cannot be inscribed

Answer 1

The correct option is A $\frac{12}{\sqrt{5}}cm$

Let $h$ be the height of rhombus
Area of Rhombus $=\frac{1}{2}\times 12\times 24$
$\frac{1}{2}\times 12\times 24=6\sqrt{5}\times h$
$h=\frac{1}{2}\times \frac{12\times 24}{6\sqrt{5}}$
$h=2r=\frac{24}{\sqrt{5}}$
$r=\frac{12}{\sqrt{5}}$