Answer:
[tex]x=4[/tex]
Step-by-step explanation:
Before we find x, we need to set up this triangle a little more. We need to find the triangle's altitude before we can solve for x. We will use the heartbeat method to find the altitude.
Let altitude = y; solve for y:
[tex]\frac{2}{y}=\frac{y}{6}[/tex]
[tex]y^2=12[/tex]
[tex]y=\sqrt{12}[/tex]
[tex]y=2\sqrt{3}[/tex]
Now that we know the altitude, we can use the Pythagorean Theorem to find the hypotenuse (x).
[tex]a^2+b^2=c^2[/tex]
[tex]2^2+(2\sqrt{3})^2=c^2[/tex]
[tex]4+12=c^2[/tex]
[tex]c^2=16[/tex]
[tex]c=4[/tex]
Since c and x are the same; c is just the hypotenuse in the Pythagorean Theorem.
[tex]x=4[/tex]
