In a triangle ABC, a point D lies on AB and points E and F…

In a triangle ABC, a point D lies on AB and points E and F lie on BC such that DF is parallel to AC and DE is parallel to AF. If BE = 4 cm. EF = 6cm, then find the length (in cm) of BC.

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e 25.

Here DE is parallel to AF so one can say that,

$\triangle$ BDE and $\triangle$ ABF are similar by AA similarity.

BE/BF = BD/AB = 4/10 = 2/5.............(1)

Here DF is parallel to AC so one can say that,

$\triangle$ BDF is similar to $\triangle$ ABC by AA similarity.

BF/BC = BD/BA = 10/x..............(2)

From eq 1 and 2 we get,

2/5 = 10/x

x = 50/2 = 25 cm.

SSC CGL 2021 PYQ — Question 72