Answer:
[tex]\sqrt{246}[/tex]
Step-by-step explanation:
The scale factor is [tex]\frac{4\sqrt{138} }{\sqrt{138}}[/tex] = 4
If AB = 6[tex]\sqrt{3}[/tex] then AC = 24[tex]\sqrt{3}[/tex] 4 times longer.
Using a² + b² = c² substitute a = 4[tex]\sqrt{138}[/tex], b = 24[tex]\sqrt{3}[/tex], and c = DC = x
[tex](4\sqrt{138})^2 + (24\sqrt{3} )^2= x^2[/tex]
2208 + 1728 = x²
3936 = x²
[tex]\sqrt{3936} = x[/tex]
4[tex]\sqrt{246[/tex] this is the length of DC
Now the length of EC is 4 times shorter, so EC = [tex]\sqrt{246}[/tex]
