Answer:
![2√(22)](https://img.qammunity.org/2022/formulas/mathematics/high-school/nz1sjp4jbcqkkho7oq9cojfcianppiu2ci.png)
Explanation:
Pythagorean theorem:
, 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.
![9^(2) +b^(2) = 13^(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/f5qb8ezmbkh6g90l6s7sdsir8yacol4ee7.png)
![81 +b^(2) = 169](https://img.qammunity.org/2022/formulas/mathematics/high-school/sj6a7gcy3hupq1704v5vnt9x3mc13llwab.png)
Since we don't know what
is, we're going to isolate it by subtracting 81 on both sides
![b^(2) = 88](https://img.qammunity.org/2022/formulas/mathematics/high-school/zfh6b1k59mm8wxnj3srpo5iqgyv65f0pu8.png)
We have to square root both sides in order to find out b (or x in the problem).
![\sqrt{b^(2)} = √(88)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ihinw2viez5b9q50nbefa2h88rmbu0j0tb.png)
When you put this on a calculator it would result in
which is the answer d in the problem.