Question

The in-radius of an equilateral triangle is of length $3$ cm, then the length of each of its median is:

• A. $12$ cm
• B. $\frac{9}{2}$
• C. $4$ cm
• D. $9$ cm

Answer 1

Answer: (D)

$9$ cm

Since in an equilateral triangle in-centre, centroid, circum-centre and ortho-centre lie on the same point.
$\Rightarrow$ Centroid divides the median in the ratio $2:1$
$\therefore$ Length of each median $=(2+1)\times$ in-radius
$=3\times 3$ cm
$=9$ cm

Hence, option D is correct.