Answer/Explanation:
[tex] 12^2 = 16*x [/tex] (altitude to hypotenuse theorem)
Solve for x using this equation
[tex] 144 = 16x [/tex]
[tex] \frac{144}{16} = x [/tex] (division property of equality)
[tex] 9 = x [/tex]
[tex] x = 9 [/tex]
[tex] y^2 = 12^2 + x^2 [/tex] (pythagorean theorem)
[tex] y^2 = 12^2 + 9^2 [/tex] (substitution)
[tex] y^2 = 144 + 81 [/tex]
[tex] y^2 = 225 [/tex]
[tex] \sqrt{y^2} = \sqrt{225} [/tex]
[tex] y = 15 [/tex]
[tex] z^2 = (x + 16)^2 - y^2 [/tex] (pythagorean theorem)
[tex] z^2 = (9 + 16)^2 + 15^2 [/tex] (substitution)
[tex] z^2 = 25^2 + 15^2 [/tex]
[tex] z^2 = 625 + 225 [/tex]
[tex] z^2 = 850 [/tex]
[tex] \sqrt{z^2} = \sqrt{850} [/tex]
[tex] z = \sqrt{25*34} [/tex]
[tex] z = 5\sqrt{34} [/tex]
