Question

Find the measure of X, Y and Z in simplest form:

Answer 1

Answer/Explanation:

$12^2 = 16*x$ (altitude to hypotenuse theorem)

Solve for x using this equation

$144 = 16x$

$\frac{144}{16} = x$ (division property of equality)

$9 = x$

$x = 9$

$y^2 = 12^2 + x^2$ (pythagorean theorem)

$y^2 = 12^2 + 9^2$ (substitution)

$y^2 = 144 + 81$

$y^2 = 225$

$\sqrt{y^2} = \sqrt{225}$

$y = 15$

$z^2 = (x + 16)^2 - y^2$ (pythagorean theorem)

$z^2 = (9 + 16)^2 + 15^2$ (substitution)

$z^2 = 25^2 + 15^2$

$z^2 = 625 + 225$

$z^2 = 850$

$\sqrt{z^2} = \sqrt{850}$

$z = \sqrt{25*34}$

$z = 5\sqrt{34}$