Answer:
The value of x,y and z is;
![\begin{gathered} x=5.92 \\ y=7.75 \\ z=9.17 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D5.92%20%5C%5C%20y%3D7.75%20%5C%5C%20z%3D9.17%20%5Cend%7Bgathered%7D)
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;
![\frac{x}{5}=\frac{7}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B5%7D%3D%5Cfrac%7B7%7D%7Bx%7D)
solving for x; cross multiply
![\begin{gathered} x^2=7(5) \\ x^2=35 \\ x=\sqrt[]{35} \\ x=5.92 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%3D7%285%29%20%5C%5C%20x%5E2%3D35%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B35%7D%20%5C%5C%20x%3D5.92%20%5Cend%7Bgathered%7D)
To get the value of y and z, we can use Pythagorean theorem or still applt the method above;
![\begin{gathered} \frac{y}{5}=\frac{(5+7)}{y} \\ y^2=5(12) \\ y^2=60 \\ y=\sqrt[]{60} \\ y=7.75 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7By%7D%7B5%7D%3D%5Cfrac%7B%285%2B7%29%7D%7By%7D%20%5C%5C%20y%5E2%3D5%2812%29%20%5C%5C%20y%5E2%3D60%20%5C%5C%20y%3D%5Csqrt%5B%5D%7B60%7D%20%5C%5C%20y%3D7.75%20%5Cend%7Bgathered%7D)
For z;
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bz%7D%7B7%7D%3D%5Cfrac%7B%285%2B7%29%7D%7Bz%7D%20%5C%5C%20z%5E2%3D7%285%2B7%29%20%5C%5C%20z%5E2%3D7%2812%29%20%5C%5C%20z%5E2%3D84%20%5C%5C%20z%3D%5Csqrt%5B%5D%7B84%7D%20%5C%5C%20z%3D9.17%20%5Cend%7Bgathered%7D)
The value of x,y and z is;
Is it adding ,subracting,mulipty,or divide
We need a picture to see what to solve