Answer:
The value of x,y and z is;
[tex]\begin{gathered} x=5.92 \\ y=7.75 \\ z=9.17 \end{gathered}[/tex]
Explanation:
We want to find the values of x,y and z.
Given the figure in the attached image;
The triangle is divided into two similar triangles and the ratio of their sides will be equal;
[tex]\frac{x}{5}=\frac{7}{x}[/tex]
solving for x; cross multiply
[tex]\begin{gathered} x^2=7(5) \\ x^2=35 \\ x=\sqrt[]{35} \\ x=5.92 \end{gathered}[/tex]
To get the value of y and z, we can use Pythagorean theorem or still applt the method above;
[tex]\begin{gathered} \frac{y}{5}=\frac{(5+7)}{y} \\ y^2=5(12) \\ y^2=60 \\ y=\sqrt[]{60} \\ y=7.75 \end{gathered}[/tex]
For z;
[tex]\begin{gathered} \frac{z}{7}=\frac{(5+7)}{z} \\ z^2=7(5+7) \\ z^2=7(12) \\ z^2=84 \\ z=\sqrt[]{84} \\ z=9.17 \end{gathered}[/tex]
The value of x,y and z is;
[tex]\begin{gathered} x=5.92 \\ y=7.75 \\ z=9.17 \end{gathered}[/tex]
