for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, (a^{2}+b^{2}=c^{2}), where (c) is the hypotenuse. Here, (c = 13), (a=x), (b = 7). So (x^{2}+7^{2}=13^{2}).

Step2: Rearrange the equation to solve for (x)

(x^{2}=13^{2}-7^{2}). Calculate (13^{2}=169) and (7^{2}=49). Then (x^{2}=169 - 49=120).

Step3: Find the value of (x)

(x=\sqrt{120}\approx10.95)

Answer:

(10.95)