Question

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

2. What is the value of y in the figure?
3. What is the value of z in the figure?

Answer 1

`x=6√(5)\\ \\y=3√(5)\\ \\z=6`

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√(5)`

and

`y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3√(5)`