SSC CGL 2021 PYQ — Question 74

The correct answer is option 3 i.e. 7.2

Given :

∠A = 90° and AD Ʇ BC  at D

 AB = 12cm and AC = 16 cm

Concept used :

Pythagoras theorem :

(Hypotenuse) = Perpendicular² + base²      ----- (1)

Similarity of triangles

Calculations :

Using equation (1), we get

⇒ BC² = AB² + AC² 

⇒ BC² = 144 + 256

⇒ BC = $\sqrt{400}$

⇒ BC = 20 cm

Now using the similarity of triangle in ABC and DBA

⇒ $\frac{BC}{AB}= \frac{AB}{BD}= \frac{AC}{AD}$

⇒ BC = AB²/BD

⇒ BD = (12 × 12)/20

⇒ BD = 144/20

⇒ BD = 7.2 cm