Question

find x. 18 2 2√9 9√2

Explanation:

Step1: Use Pythagorean theorem

For a right - angled isosceles triangle with legs \(x\) and hypotenuse \(c = 18\), by Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(a = b=x\), so \(x^{2}+x^{2}=18^{2}\).

Step2: Simplify the equation

\(2x^{2}=324\), then \(x^{2}=\frac{324}{2}=162\).

Step3: Solve for \(x\)

\(x=\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\)

Answer:

\(9\sqrt{2}\)