Question

find the length of side x in simplest radical form with a rational denominator.
(right triangle with legs x (marked) and one leg (marked), hypotenuse 4)
answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle: two legs are equal ($x$ each), hypotenuse = 4.

Step2: Apply Pythagorean theorem

$$x^2 + x^2 = 4^2$$

Step3: Simplify the equation

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

Step4: Solve for x, rationalize

$$x = \sqrt{8} = 2\sqrt{2}$$
(No rationalization needed here as denominator is 1)

Answer:

$2\sqrt{2}$