In ΔDEF, the bisector of ∠D intersects side EF at point N. If DE = 36 cm, DF = 40 cm and EF = 38 cm, then the length (in cm) of NF is ________.

Correct option is B

Given:

In triangle ΔDEF, DE = 36 cm, DF = 40 cm, EF = 38 cm.

The angle bisector of ∠D intersects side EF at point N.

Theorem Used: 

The Angle Bisector Theorem states that the angle bisector of ∠D divides the opposite side EF into two segments, EN and NF, such that:

​$$\frac{DE }{DF} = \frac{EN }{ NF}$$​​

Solution:

According to the Angle Bisector Theorem:

​$$\frac{DE }{DF} = \frac{EN }{ NF}$$​​

Substitute the given values:

​$$\frac{36 }{ 40} = \frac{EN }{NF}$$​​

Simplify the ratio:

​$$\frac{9 }{10 }= \frac{EN }{ NF}$$​​

Let NF = x. Therefore, EN = $$(\frac{9}{10}) × x.$$​​

Now, since EF = EN + NF = 38 cm:

​$$\frac{(9}{10}) × x + x = 38 \\\ \\=> \frac{(9x + 10x) }{ 10 }= 38 \\\ \\=> 19x = 380 \\\ \\=> x = \frac{380 }{19} \\\ \\=> x = 20 cm$$​​

The length of NF is 20 cm.