Answer:
[tex]AB=4\sqrt{5}[/tex] (Which is the same as [tex]\sqrt{80}[/tex])
Step-by-step explanation:
In order to find the length of AB, we first need to know the length of AC.
The length of the sides for ACD are
[tex]a=2\\b=?\\c=10[/tex]
Knowing these values, we can plug them into the pythagorean theorem and solve for the missing side, b
[tex]a^2+b^2=c^2\\\\b^2=c^2-a^2\\\\b=\sqrt{c^2-a^2} \\\\b=\sqrt{(10)^2-(2)^2} \\\\b=\sqrt{100-4}\\ \\b=\sqrt{96}[/tex]
This means that [tex]AC=\sqrt{96}[/tex]
Now, let us find the values of a,b and c for our second triangle
[tex]a=4\\b=x\\c=\sqrt{96}[/tex]
And now time for the pythagorean theorem
[tex]b=\sqrt{c^2-a^2} \\\\b=\sqrt{(\sqrt{96})^2-(4)^2 } \\\\b=\sqrt{96-16}\\\\b=\sqrt{80} \\\\b=4\sqrt{5}[/tex]
This means that [tex]AB=4\sqrt{5}[/tex] (Which is the same as [tex]\sqrt{80}[/tex])
