Question

the triangle below is isosceles. find the length of side ( x ) in simplest radical form with a rational denominator.

Explanation:

Step1: Identify equal sides

This is a right isosceles triangle, so the two legs are equal, both length 10.

Step2: Apply Pythagorean theorem

The Pythagorean theorem states $a^2 + b^2 = c^2$, where $a$ and $b$ are legs, $c$ is hypotenuse $x$.
$$10^2 + 10^2 = x^2$$

Step3: Calculate squared terms

$$100 + 100 = x^2$$
$$200 = x^2$$

Step4: Solve for x, simplify radical

$$x = \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2}$$

Answer:

$10\sqrt{2}$