Answer:
x = [tex]\sqrt{6}[/tex]
Step-by-step explanation:
Since the given triangle is equilateral the all 3 sides would be:
[tex]\sqrt{6} +\sqrt{6}[/tex] or [tex]\sqrt{12}[/tex]. Now we know that the base of the right triangle is [tex]\sqrt{6}[/tex] and the hypotenuse is [tex]\sqrt{12}[/tex]. Therefore we can say;
A² + B² = C²
([tex]\sqrt{6}[/tex])² + x² = ([tex]\sqrt{12}[/tex])²
6 + x² = 12
x² = 12 - 6
x² = 6
x = [tex]\sqrt{6}[/tex]
Therefore; x = [tex]\sqrt{6}[/tex] is the length of x, in simplest radical form.
