Answer:
[tex]z =3\sqrt{13}[/tex]
Step-by-step explanation:
In the figure you can identify up to 3 straight triangles.
To solve the problem, write the Pythagorean theorem for each triangle.
Triangle 1
[tex]13^2 = z^2 + x^2[/tex]
Triangle 2
[tex]z^2 = y^2 + 9^2[/tex]
Triangle 3
[tex]x^2 = y^2 + 4^2[/tex]
Now substitute equation 2 and equation 3 in equation 1 and solve for y.
[tex]13^2 = y^2 + 9^2 + y^2 + 4^2[/tex]
[tex]13^2 = 2y^2 + 9^2 + 4^2[/tex]
[tex]169 = 2y^2 + 81 + 16[/tex]
[tex]2y^2 =72[/tex]
[tex]y^2 =36[/tex]
[tex]y =6[/tex]
substitute the value of y in the second equation and solve for z
[tex]z^2 = 6^2 + 9^2[/tex]
[tex]z^2 = 36 + 81[/tex]
[tex]z^2 = 117[/tex]
[tex]z = \sqrt{117}[/tex]
[tex]z =3\sqrt{13}[/tex]
