Question

WILL MEDAL
Given Angle 1 = Angle 2,
Find X

Answer 1

Do you know the triangle angle bisector theorem?

Answer 2

The bisector of an angle pf a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the adjacent sides.

Answer 3

In the triangle of the above figure, if angles 1 and 2 are congruent, then
a/b = c/d

Answer 4

In your case you have

\( \dfrac{3}{x - 4} = \dfrac{x}{4} \)

Answer 5

Now solve the proportion for x.

Answer 6

...

Answer 7

6 or -2

Answer 8

@dan815

Answer 9

@uri

Answer 10

@math1234

Answer 11

@Falling_In_Katt You solved the proportion correctly.
The solutions to the equation are 6 and -2.
In this problem, x represents a length. A length can't be negative, so discard the negative solution, -2, and keep only the positive solution 6.