ABC is a triangle in which ∠A = 90°. Let P be any point on side AC. If BC = 10 cm, AC = 8 cm and BP = 9 cm, then AP = ?

A. $$2\sqrt 5 $$ cm

B. $$3\sqrt 5 $$ cm

C. $$2\sqrt 3 $$ cm

D. $$3\sqrt 3 $$ cm

Answer: Option B

Solution(By Examveda Team)

According to question,
BC = 10 cm, AC = 8 cm, BP = 9 cm
In ΔCAB,
BC² = AB² + AC²
10² = AB² + 8²

AB² = 100 - 64
AB² = 36
AB = 6 cm
In ΔPAB
BP² = AB² + AP²
9² = 6² + AP²
AP² = 81 - 36
AP² = 45
AP = $$3\sqrt 5 $$  cm