In triangle DEF, the bisector of angle D intersects side EF at point N. Given DE = 36 cm, DF = 40 cm, and EF = 38 cm, find the length of NF in cm.

Question

Accepted Answer

According to the Angle Bisector Theorem, the bisector of an angle in a triangle divides the opposite side into segments proportional to the adjacent sides.

Given triangle DEF with angle bisector DN intersecting EF at N:

DE / DF = EN / NF

Given:
DE = 36 cm
DF = 40 cm
EF = 38 cm

Let EN = x cm, then NF = 38 - x cm.

Using the theorem:
36 / 40 = x / (38 - x)

Cross-multiplied:
36(38 - x) = 40x
1368 - 36x = 40x
1368 = 40x + 36x
1368 = 76x
x = 1368 / 76 = 18 cm

So, EN = 18 cm
NF = 38 - 18 = 20 cm

Therefore, the length of NF is 20 cm.

Answer

Answer

Answer