micawalk4530
micawalk4530 micawalk4530
  • 21-11-2021
  • Mathematics
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What is the exact length of AB?

What is the exact length of AB class=

Respuesta :

jimrgrant1 jimrgrant1
  • 21-11-2021

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]

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