Answer:
[tex]x=3\sqrt{5}[/tex]
Step-by-step explanation:
Right Triangles
Right triangles have one of its interior angles with a measure of 90°.
In right triangles the Pythagora's Theorem is satisfied.
Being c the longest side (hypotenuse), a and b the shorter sides (the legs), then:
[tex]c^2=a^2+b^2[/tex]
We have modified the image to include some known data. Both triangles are congruent since they share one side, have a right angle, and have the same base length.
This means the value of x can be calculated as the hypotenuse of the triangle 3-6-x:
[tex]x^2=3^2+6^2=9+36=45[/tex]
[tex]x=\sqrt{45}=\sqrt{9*5}[/tex]
[tex]\boxed{x=3\sqrt{5}}[/tex]
