Question

Solve for x, y, and z. Enter the integer that is under each radical.

Answer 1

Answer:

$x=\sqrt{10}$

$y = \sqrt {14}$

$z = \sqrt {35}$

Step-by-step explanation:

By geometric mean theorem:

$x=\sqrt{2\times 5}$

$x=\sqrt{10}$

By Pythagoras Theorem:

$y^2 = x^2 + 2^2$

$y^2 = (\sqrt{10}) ^2 + 2^2$

$y^2 = 10 + 4$

$y^2 = 14$

$y = \sqrt {14}$

Again by Pythagoras Theorem:

$z^2 = x^2 + 5^2$

$z^2 = (\sqrt{10}) ^2 + 5^2$

$z^2 = 10 + 25$

$z^2 = 35$

$z = \sqrt {35}$