Question

12/26 find x.

Explanation:

Step1: Apply Pythagorean theorem

Let the two legs of the right - triangle be \(x\) and \(x\) (since it's an isosceles right - triangle, as the two non - hypotenuse sides are equal in length in the given square - related right - triangle), and the hypotenuse \(c = 6\sqrt{2}\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), here \(a = b=x\), so \(x^{2}+x^{2}=(6\sqrt{2})^{2}\).

Step2: Simplify the equation

Combining like terms, \(2x^{2}=72\) (because \((6\sqrt{2})^{2}=6^{2}\times(\sqrt{2})^{2}=36\times2 = 72\)).

Step3: Solve for \(x^{2}\)

Dividing both sides of \(2x^{2}=72\) by 2, we get \(x^{2}=36\).

Step4: Solve for \(x\)

Taking the square root of both sides, \(x = 6\) (we consider the positive value since \(x\) represents a length).

Answer:

6