Question

BD BIsects <ABC and D lies on AC
IF AB=6. BC= 14. AC=14
Find AD

WE KNOW THE ANSWER IS 4.2.
Please show me how to get there

Thank you

Answer 1

Answer on Question#38749 – Math – Geometry

BD bisects &lt;ABC and D lies on AC

If AB=6. BC=14. AC=14

Find AD

Solution:

The angle bisector theorem states that the ratio of the length of the line segment AD to the length of segment DC is equal to the ratio of the length of side AB to the length of side BC:

$$\frac {A D}{D C} = \frac {A B}{B C}$$

Let $AD = x$ , then $DC = 14 - x$ , so:

$$\frac {x}{1 4 - x} = \frac {6}{1 4}$$

Multiplying both sides on $7(14 - x)$ :

$$7 x = 3 (1 4 - x)$$

Expanding:

$$7 x = 4 2 - 3 x$$ $$1 0 x = 4 2$$

Answer: $x = 4.2$