Question

What is the value of DE if AB = 6, AD = 8, and BC = 3?
Responses
A 3.5
B 4
C 4.5
D 5

Answer 1

To find the value of DE, we can use the angle bisector theorem. The angle bisector theorem states that in a triangle, if an angle bisector intersects the opposite side (DE in this case), then it divides the opposite side into segments that are proportional to the lengths of the other two sides (AB and BC).

In this case, we can set up an equation using the angle bisector theorem:

(AD / DB) = (AE / EC)

Plug in the given values:

(8 / DB) = (AE / 3)

Multiply both sides by 3:

24 / DB = AE

We know that AB = 6, so AE + EC = AB.

AE + 3 = 6

Subtract 3 from both sides:

AE = 3

Now we can plug in this value into the equation we set up:

24 / DB = 3

Multiply both sides by DB:

24 = 3 * DB

Divide both sides by 3:

8 = DB

So DE = DB + EC = 8 + 3 = 11.

Therefore, the value of DE is 11.