Answer:
AB = 5[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
AB² + BC² = AC²
AB² + (2[tex]\sqrt{3}[/tex] )² = (9[tex]\sqrt{2}[/tex] )²
AB² + 12 = 162 ( subtract 12 from both sides )
AB² = 150 ( take square root of both sides )
AB = [tex]\sqrt{150}[/tex] = [tex]\sqrt{25(6)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{6}[/tex] = 5[tex]\sqrt{6}[/tex]
