Question

find the missing side of the right triangle.
leave your answer in simplified radical form.
$x = \\\\$
$4\sqrt{6}$ $12$ $\sqrt{146}$ $2\sqrt{73}$ $6$

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $a=5$, $b=x$, $c=11$.
$$5^2 + x^2 = 11^2$$

Step2: Calculate squared values

Compute $5^2$ and $11^2$.
$$25 + x^2 = 121$$

Step3: Isolate $x^2$

Subtract 25 from both sides.
$$x^2 = 121 - 25 = 96$$

Step4: Simplify radical for $x$

Take square root and simplify $\sqrt{96}$.
$$x = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}$$

Answer:

$4\sqrt{6}$ ft