find the exact value of $x$.\n$x = \\square$

Explanation:

Step1: Identify the Pythagorean theorem

$$a^{2} + b^{2} = c^{2}$$

Step2: Substitute the given side lengths

$$7^{2} + 11^{2} = x^{2}$$

Step3: Calculate the squares of the numbers

$$49 + 121 = x^{2}$$

Step4: Sum the values

$$170 = x^{2}$$

Step5: Solve for x

$$x = \sqrt{170}$$

Answer:

x = \sqrt{170}