Question

the triangle below is isosceles. find the length of side ( x ) in simplest radical form with a rational denominator.
10

Explanation:

Step1: Identify triangle type

It's an isosceles right triangle, so legs are equal. One leg is 10, so the other leg is also 10.

Step2: Apply Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \). Here, \( a = 10 \), \( b = 10 \), \( c = x \). So \( x^2 = 10^2 + 10^2 \).

Step3: Calculate \( x^2 \)

\( x^2 = 100 + 100 = 200 \).

Step4: Simplify \( x \)

\( x = \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \).

Answer:

\( 10\sqrt{2} \)