Given the diagram below, Philip thinks the value of x is 9, but Mia thinks the value of x is 12. Which student is correct? Justify your answer.

Answer:
Mia is correct
Step-by-step explanation:
The outer triangle and the inner triangle are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion
[tex]\frac{2}{2+6} [/tex] = [tex]\frac{3}{x} [/tex] , that is
[tex]\frac{2}{8} [/tex] = [tex]\frac{3}{x} [/tex] ( cross- multiply )
2x = 24 ( divide both sides by 2 )
x = 12