Answer: [tex]2\sqrt{22}[/tex]
Step-by-step explanation:
Pythagorean theorem: [tex]a^{2} +b^{2} = c^{2}[/tex], where a and b are the legs and c is the hypotenuse.
We can solve for x by only using the left side of the triangle. Since we're only using the left side of the triangle, we can reduce 18 by 2 to get 9. Now we plug in our information to the equation.
[tex]9^{2} +b^{2} = 13^{2}[/tex]
[tex]81 +b^{2} = 169[/tex]
Since we don't know what [tex]b^{2}[/tex] is, we're going to isolate it by subtracting 81 on both sides
[tex]b^{2} = 88[/tex]
We have to square root both sides in order to find out b (or x in the problem).
[tex]\sqrt{b^{2}} = \sqrt{88}[/tex]
When you put this on a calculator it would result in [tex]2\sqrt{22}[/tex] which is the answer d in the problem.
