Question

find the length of side x in simplest radical form with a rational denominator.

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle: the right angle and two congruent legs (marked by ticks) mean the acute angles are $45^\circ$.

Step2: Apply Pythagorean theorem

Let the legs be $x$, hypotenuse = 4.
$$x^2 + x^2 = 4^2$$

Step3: Simplify the equation

$$2x^2 = 16$$
$$x^2 = 8$$

Step4: Solve for x, rationalize

$$x = \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$$

Answer:

$2\sqrt{2}$