Question

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

Explanation:

Step1: Find vertical side of right - triangle

The vertical side of the right - triangle formed is $15 - 9=6$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a = 4$, $b = 6$, and $c=x$. So $x=\sqrt{4^{2}+6^{2}}$.

Step3: Calculate value of $x$

$x=\sqrt{16 + 36}=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$