Question

Trying figure out to solve the problem. I went wrong somewhere. I have x=35, y=7.7, z=84

Answer 1

Answer:

The value of x,y and z is;

$\begin{gathered} x=5.92 \\ y=7.75 \\ z=9.17 \end{gathered}$

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;

$\frac{x}{5}=\frac{7}{x}$

solving for x; cross multiply

$\begin{gathered} x^2=7(5) \\ x^2=35 \\ x=\sqrt[]{35} \\ x=5.92 \end{gathered}$

To get the value of y and z, we can use Pythagorean theorem or still applt the method above;

$\begin{gathered} \frac{y}{5}=\frac{(5+7)}{y} \\ y^2=5(12) \\ y^2=60 \\ y=\sqrt[]{60} \\ y=7.75 \end{gathered}$

For z;

$\begin{gathered} \frac{z}{7}=\frac{(5+7)}{z} \\ z^2=7(5+7) \\ z^2=7(12) \\ z^2=84 \\ z=\sqrt[]{84} \\ z=9.17 \end{gathered}$

The value of x,y and z is;

$\begin{gathered} x=5.92 \\ y=7.75 \\ z=9.17 \end{gathered}$