Question

Please help me!

Explain how to find the value of x. Be sure to include the postulates, definitions, and theorems that justify your answer.

Answer 1

x = 12

Explanation:

Using the Altitude- on- Hypotenuse theorem

The 2 triangles are similar to the outside triangle and to each other, that is

Δ RQT ~ ΔSRT

Since the triangles are similar then the ratios of corresponding sides are equal, that is

`(RT)/(ST)` =
`(QT)/(RT)`, substitute values

`(x)/(9)` =
`(16)/(x)` ( cross- multiply )

x² = 144 ( take the square root of both sides )

x =
`√(144)` = 12