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

Mia is correct

Explanation:

The outer triangle and the inner triangle are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion

`(2)/(2+6)` =
`(3)/(x)` , that is

`(2)/(8)` =
`(3)/(x)` ( cross- multiply )

2x = 24 ( divide both sides by 2 )

x = 12