Question

How to solve problem 31? Solve for x y and z using ratios

Answer 1

The Solution:

Given:

Required:

Find the values for x, y, and z.

By the Similarity Theorem:

`\Delta BAD\cong\Delta CBD`

So,

`\begin{gathered} (x)/(36)=(36)/(6x) \\ \\ (x)/(36)=(6)/(x) \end{gathered}`

Cross multiply:

`\begin{gathered} x^2=36*6 \\ \\ x=√(36*6)=6√(6) \end{gathered}`

Find y by applying the Pythagorean Theorem on the right triangle CBD:

`\begin{gathered} y^2=36^2+(6√(6))^2 \\ \\ y=6√(42) \end{gathered}`

Find z:

By the Pythagorean Theorem:

`\begin{gathered} z^2=(42√(6))^2-(6√(42))^2 \\ \\ z=36√(7) \end{gathered}`

Answer:

`\begin{gathered} x=6√(6) \\ \\ y=6√(42) \\ \\ z=36√(7) \end{gathered}`