Answer:
x = 6[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
( leg of large triangle)² = (part of hypotenuse below it) × (whole hypotenuse) , so
x² = 9 × (9 + 3) = 9 × 12 = 108 ( take square root of both sides )
x = [tex]\sqrt{108}[/tex] = [tex]\sqrt{36(3)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{3}[/tex] = 6[tex]\sqrt{3}[/tex]
