Correct Answer: $5 \sqrt{5} $ cm

Solution :
Given,
Median NA = 15 cm
Median OB = 15 cm
Medians intersect at right angles at point S
Theorem: The medians of a triangle intersect each other at the centroid, which divides each median in the ratio 2 : 1.
As S is the point where the medians intersect, it divides each median in a 2 : 1 ratio, with the longer section towards the midpoint of the side.
$\therefore$ the length of OS (longer section of OB) = $\frac{2}{3} ×$15 = 10 cm
And, SA (shorter section of NA) = $\frac{1}{3} ×$15 = 5 cm.
Since the medians intersect at right angles
Applying the Pythagorean theorem,
⇒ OA ² = OS ² + SA ²
⇒ OA ² = (10 cm) ² + (5 cm) ²
⇒ OA ² = 100 cm ² + 25 cm ²
⇒ OA ² = 125 cm ²
⇒ OA = $\sqrt{125}$ cm ²
⇒ OA = 5$\sqrt5$ cm
Hence, the correct answer is $5\sqrt5$ cm.