Question

find x.options: $sqrt{2}$, 12, 6, $sqrt{3}$

Explanation:

Step1: Identify triangle type

This is a right isosceles triangle (legs marked equal, right angle), so legs are length $x$, hypotenuse is $6\sqrt{2}$.

Step2: Apply Pythagorean theorem

For right triangles: $a^2 + b^2 = c^2$. Substitute $a=b=x$, $c=6\sqrt{2}$.
$$x^2 + x^2 = (6\sqrt{2})^2$$

Step3: Simplify both sides

Left: $2x^2$. Right: $6^2 \times (\sqrt{2})^2 = 36 \times 2 = 72$.
$$2x^2 = 72$$

Step4: Solve for $x^2$

Divide both sides by 2.
$$x^2 = \frac{72}{2} = 36$$

Step5: Solve for $x$

Take positive square root (length is positive).
$$x = \sqrt{36} = 6$$

Answer:

6