Question

Suppose DK is an angle bisector of △DEF. Given: EK=2, FK=5, DF=10. Find DE.

Answer 1

Answer:

$DE=4$

Step-by-step explanation:

We have been provided a graph of a triangle and we are asked to find the length of segment DE.

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

By angle bisector theorem we can set proportions of the given sides as:

$\frac{DE}{EK}=\frac{DF}{FK}$

Upon substituting our given values in above proportion we will get,

$\frac{DE}{2}=\frac{10}{5}$

Upon multiplying both sides of our equation by 2 we will get,

$\frac{DE}{2}\times 2=2\times \frac{10}{5}$

$DE=2\times 2$

$DE=4$

Therefore, the length of segment DE is 4 units.