Answer:
x = 6
Step-by-step explanation:
Since, ∠1 ≅ ∠2
By angle bisector theorem,
[tex]\frac{AB}{BD}=\frac{AC}{CD}[/tex]
By substituting the measures of each side in the given ratio of the sides,
[tex]\frac{3}{x-4}=\frac{x}{4}[/tex]
12 = x(x - 4)
12 = x² - 4x
x² - 4x - 12 = 0
x² - 6x + 2x - 12 = 0
x( x - 6) + 2(x - 6) = 0
(x + 2)(x - 6) = 0
x = -2, 6
Since, measure of the sides can't be negative, x can not be negative.
Therefore, x = 6 will be the answer.
