Question : 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:
Option 1: 19.5 cm
Option 2: 26 cm
Option 3: 20.5 cm
Option 4: 13 cm
Correct Answer: 13 cm
Solution :
Given: AB = 19 cm, AC = 22 cm
BE and CF are perpendicular to each other.
We know that
AB
2
+ AC
2
= 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
Hence, the correct answer is 13 cm.
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