Answer:
[tex]x=3\sqrt{2}\\[/tex]
Step-by-step explanation:
Since the smaller triangles have a side of the same length, they share one side, and the included angle is 90°, the triangles are congruent.
This means the length of the side to the left is also x as shown in the image below.
The bigger triangle is also right and has side lengths of x, x, and 6 (the hypotenuse), thus:
[tex]x^2+x^2=6^2[/tex]
Operating:
[tex]2x^2=36[/tex]
[tex]x^2=18[/tex]
Since 18=9*2
[tex]x=\sqrt{9*2}[/tex]
[tex]\mathbf{x=3\sqrt{2}}[/tex]
The options are not clear enough, so I cannot make a choice.
