If in a triangle ABC BE and CF are two medians...

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If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19 cm and AC = 22 cm then the length of BC is

A. 20.5 cm

B. 19.5 cm

C. 26 cm

D. 13 cm

Answer: Option D

Solution (By Examveda Team)

Given

AB = 19 cm, AC = 22 cm,
∵ BE ⊥ CF (Given), [Medians CF & BE are perpendicular to each other]
In this case
We know,
AB² + AC² = 5(BC)²
⇒ (19)² + (22)² = 5(BC)²
⇒ 361 + 484 = 5(BC)²
⇒ 845 = 5(BC)²
⇒ (BC)² = 169
⇒ BC = 13 cm

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