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

A. $$2\sqrt 5 $$  cm

B. $$5\sqrt 2 $$  cm

C. $$10\sqrt 2 $$  cm

D. $$4\sqrt 5 $$  cm

Answer: Option A

Solution(By Examveda Team)

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