Question

What is the value of x? Triangle ABC. Segment AD bisects angle A. The length of side AB is 28. The length of segment BD is 14. The length of side AC is 25. The length of segment CD is unknown and is labeled x. Enter your answer, as a decimal, in the box. x =

Answer 1

Explanation:

To find the value of x, we can use the Angle Bisector Theorem, which states that in a triangle, a line segment that bisects an angle divides the opposite side into segments that are proportional to the other two sides.

In this case, segment AD bisects angle A, so we can set up the following proportion:

BD/DC = AB/AC

Plugging in the given values, we have:

14/DC = 28/25

To solve for DC (segment CD), we can cross-multiply:

28 * DC = 14 * 25

Simplifying further:

DC = (14 * 25) / 28

DC ≈ 12.5

Therefore, the length of segment CD is approximately 12.5.