Question

In triangle DEF, DK is the angle bisector of angle EDF. If EK=2, FK=5, and DF=10, what is the length of DE?

Answer 1

Answer:

4 units

Step-by-step explanation:

In triangle DEF, DK is the angle bisector of angle EDF.

Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides.

Hence,

$\dfrac{DE}{DF}=\dfrac{EK}{KF}$

Thus,

$\dfrac{DE}{10}=\dfrac{2}{5}\\ \\5DE=2\cdot 10\\ \\5DE=20\\ \\DE=4$