Question : In a triangle DEF, DP is the bisector of $\angle D$, meeting EF at P. If DE = 14 cm, DF = 21 cm and EF = 9 cm, find EP.
Option 1: 3.6 cm
Option 2: 5.4 cm
Option 3: 6.3 cm
Option 4: 2.7 cm
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Correct Answer: 3.6 cm
Solution :
To find EP, we can use the angle bisector theorem, which states that the angle bisector of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
Given: DE = 14 cm, DF = 21 cm and EF = 9 cm
DP is the bisector of $\angle D$
Now,
$\frac{EP}{PF} = \frac{DE}{DF}$
Substituting the given values, we get:
$\frac{EP}{9 - EP} = \frac{14}{21}$
⇒ 21 EP = 126 – 14 EP
⇒ 35 EP = 126
⇒ EP = $\frac{126}{35}$
⇒ EP = 3.6
Hence, the correct answer is 3.6 cm.
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