The Solution:
Given:
Required:
Find the values for x, y, and z.
By the Similarity Theorem:
[tex]\Delta BAD\cong\Delta CBD[/tex]
So,
[tex]\begin{gathered} \frac{x}{36}=\frac{36}{6x} \\ \\ \frac{x}{36}=\frac{6}{x} \end{gathered}[/tex]
Cross multiply:
[tex]\begin{gathered} x^2=36\times6 \\ \\ x=\sqrt{36\times6}=6\sqrt{6} \end{gathered}[/tex]
Find y by applying the Pythagorean Theorem on the right triangle CBD:
[tex]\begin{gathered} y^2=36^2+(6\sqrt{6)}^2 \\ \\ y=6\sqrt{42} \end{gathered}[/tex]
Find z:
By the Pythagorean Theorem:
[tex]\begin{gathered} z^2=(42\sqrt{6})^2-(6\sqrt{42})^2 \\ \\ z=36\sqrt{7} \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} x=6\sqrt{6} \\ \\ y=6\sqrt{42} \\ \\ z=36\sqrt{7} \end{gathered}[/tex]
