solve for $x$. leave your answer in simplest radical form.

Explanation:

Step1: Find the height of the triangle

Use the Pythagorean theorem (a^{2}+b^{2}=c^{2}). Let the height be (h). For the larger right - triangle with hypotenuse (c = 10) and base (a=9), we have (h=\sqrt{10^{2}-9^{2}}). [h=\sqrt{100 - 81}=\sqrt{19}]

Step2: Solve for (x)

Now, consider the right - triangle with height (h=\sqrt{19}) and base (4). Using the Pythagorean theorem again ((x) is a side of a right - triangle), (x=\sqrt{(\sqrt{19})^{2}-4^{2}}). [x=\sqrt{19 - 16}=\sqrt{3}]

Answer:

(x = \sqrt{3})