The relationship between the variables x, y and z is an illustration of similar triangles
The values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]
How to determine the values of x, y and z
Right triangles are triangles with an angle measure of 90 degrees, and we have the following equivalent ratio from the triangle
[tex]x : 9 = 4 : x[/tex]
Express as fraction
[tex]\frac x9 = \frac 4x[/tex]
Cross multiply
[tex]x^2 = 36[/tex]
Take the square root of both sides
[tex]x = 6[/tex]
The value of y is then calculated using the following Pythagoras theorem
[tex]y = \sqrt{9^2 + x^2[/tex]
This gives
[tex]y = \sqrt{9^2 + 6^2[/tex]
[tex]y = \sqrt{117[/tex]
The value of z is then calculated using the following Pythagoras theorem
[tex]z = \sqrt{4^2 + x^2[/tex]
This gives
[tex]z = \sqrt{4^2 + 6^2[/tex]
[tex]z = \sqrt{52[/tex]
Hence, the values of x, y and z are 6, [tex]\sqrt{117}[/tex] and [tex]\sqrt{52[/tex]
Read more about triangles at:
https://brainly.com/question/17972372
