Question

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 1

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

$\frac{2}{2+6}$ = $\frac{3}{x}$ , that is

$\frac{2}{8}$ = $\frac{3}{x}$ ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12