Answer:
x = 12
Step-by-step 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
[tex]\frac{RT}{ST}[/tex] = [tex]\frac{QT}{RT}[/tex], substitute values
[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
