SSC CGL 2024 PYQ — Question 55

The correct answer is option 2 i.e. 20.

According to the given question,

Let the length of NF be x am.

⇒ EN = 38 - x

Angle Bisectore Theorem: According to this theorem, when an angle bisector cuts the opposite side at a point, then the ratio of the parts of the opposite side is equal to the ratio of the sides adjacent to the parts respectively.

In the above figure, applying angle bisector theorem,

${EN \over NF} = {DE \over DF}$

⇒ ${(38 - x) \over x} = { 36 \over 40}$

⇒ ${(38 - x) \over x} = { 9 \over 10}$

⇒ 10(38 - x) = 9x

⇒ 380 - 10x = 9x

⇒ 19x = 380

⇒ x = 20

Hence the length (in cm) of NF is 20.