Answer: x= 4.5, y=3.6, z=6.5
Step-by-step explanation:
To find : x, y and z.
First label the triangle as A,B,C and D (as in the picture below).
ΔABC , ΔACD and ΔABD both are right triangles.
In ΔABC ,
[tex]y^2=3^2+2^2[/tex] [By Pythagoras theorem]
[tex]\Rightarrow\ y^2=13\\\\\Rightarrow\ y=\sqrt{13}\approx3.6[/tex]
In ΔACD ,
[tex]AD^2=3^2+x^2\\\\\Rightarrow\ AC^2=9+x^2 \ \ ...(i)[/tex] [By Pythagoras theorem]
In ΔABC ,
[tex]y^2+AC^2=(2+x)^2\\\\\Rightarrow\ AC^2=(2+x)^2-y^2\ \ ...(ii)[/tex]
From (i) and (ii), we get
[tex]9+x^2=(2+x)^2-y^2\\\\\Rightarrow\ 9+x^2=4+x^2+4x-(3.6)^2\\\\\Rightarrow\ 9=4+4x-12.96\\\\\Rightarrow\ 4x=9-4+12.96\\\\\Rightarrow 4x= 17.96\\\\\Rightarrow\ x=\dfrac{17.96}{4}\\\\\Rightarrow\ x=4.49\approx4.5[/tex]
Z = 2+x= 2+4.5 =6.5
Hence, x= 4.5, y=3.6, z=6.5
