BL and CM are medians of ΔABC right-angled at A and BC = 5 cm. If BL = 3 5 2 cm, then the length of CM is

Answer: Option A

According to question,

According to figure, when two medians intersect each other in a right angled triangle then we use this equation.
⇒ 4 (BL² + CM²) = 5BC²
⇒ 4 × $${\left(\frac{3\sqrt{5}}{2}\right)}^2$$  + 4CM² = 5BC²
⇒ 45 + 4CM² = 125
⇒ CM² = $$\frac{125-45}{4}$$
⇒ CM² = 20
⇒ CM = $$2\sqrt{5}$$  cm