Question

1. What is the value of x in the figure?

Answer 1

Answer:

$x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6$

Step-by-step explanation:

The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so

$z^2=12\cdot 3\\ \\z^2=36\\ \\z=6$

By the Pythagorean theorem,

$x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}$

and

$y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}$