If Δ ABC, D and E are points on the sides BC and AB, respectively, such that ∠ ACB = ∠ DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2, then BC is equal to:

If Δ ABC, D and E are points on the sides BC and AB…

If $\Delta$ ABC, D and E are points on the sides BC and AB, respectively, such that $\angle$ ACB = $\angle$ DEB. If AB = 12 cm, BE = 5 cm and BD : CD = 1 : 2, then BC is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 6 $\sqrt{5}$ cm.

In $\Delta$ ABC and $\Delta$ BDE,

$\angle$ ACB = $\angle$ DEB , $\angle$ B is common,

so one can say that $\Delta$ ABC and $\Delta$ BDE are similar by AA criteria.

BD : AB = DE : AC = BE : BC

BD : AB = BE : BC

= x/12 = 5/3x

3x² = 60

x = 2 $\sqrt5$ .

BC = 3x = 3 × 2 $\sqrt5$ = 6 $\sqrt5$ .

SSC CGL 2022 PYQ — Question 65