Answer:
x = [tex]2\sqrt{2}[/tex] (or [tex]\frac{2\sqrt{2} }{1}[/tex] if it needs to be represented as a rational denominator)
Step-by-step explanation:
We know that;
1.) This triangle is equilateral, and because of the line segment it's divided into 2 right triangles.
2.) The base of the whole triangle would be 4, and the base of the right triangle would be 2, since the base is cut in half with a mid point.
Therefore we can say;
A² + B² = C²
x² + 2² = 4²
x² + 4 = 16
x² = 16 - 4
x² = 8
x = [tex]\sqrt{8}[/tex]
Simplifying this further would be;
[tex]\sqrt{8}[/tex] = [tex]\sqrt{4} * \sqrt{2}[/tex]
[tex]\sqrt{8}[/tex] = [tex]2\sqrt{2}[/tex] (or [tex]\frac{2\sqrt{2} }{1}[/tex] if it needs to be represented as a rational denominator)
Hope this helps!