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

Explanation:

Step1: Apply Pythagorean theorem

Since it's an isosceles right - triangle, let the two legs be of length (a = 10) and (b = 10), and the hypotenuse be (x). According to the Pythagorean theorem (a^{2}+b^{2}=x^{2}). Substitute (a = 10) and (b = 10) into the formula: (10^{2}+10^{2}=x^{2}), which simplifies to (100 + 100=x^{2}), so (x^{2}=200).

Step2: Solve for (x)

Take the square root of both sides: (x=\sqrt{200}). Simplify (\sqrt{200}=\sqrt{100\times2}). Using the property (\sqrt{ab}=\sqrt{a}\times\sqrt{b}(a\geq0,b\geq0)), we get (x = \sqrt{100}\times\sqrt{2}=10\sqrt{2}).

Answer:

(10\sqrt{2})