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.

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

= , that is

= ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.