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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q. 17 (page 199)

For the following figure, given that $l | | m | | n$ . Find the values of $x, y,$ and Z.

Short Answer

Expert verified

The values are $x = 8, y = 4, z = 42$ .

Step by step solution

01

Step 1- Check the figure.

Consider the figure.

02

Step 2- Step description.

Since I is parallel to n and n are bisected by m therefore calculate the values as follows:

$\begin{matrix} 5 x - 4 = 3 (x + 4) \\ 5 x - 4 = 3 x + 12 \\ 5 x - 3 x = 12 + 4 \\ 2 x = 16 \\ x = 8 \end{matrix}$

Since m is parallel to n thus,

$\begin{matrix} 6 y + 2 = 2 y^{2} - 6 \\ 2 y^{2} - 6 y - 8 = 0 \\ y^{2} - 3 y - 4 = 0 \\ y^{2} - 4 y + y - 4 = 0 \\ y (y - 4) + 1 (y - 4) = 0 \\ (y - 4) (y + 1) = 0 \\ y = - 1, 4 \end{matrix}$

03

Step 3- Step description.

Use the property of median as follows:

$\begin{matrix} 6 y + 2 = 2 y^{2} - 6 \\ z = \frac{54 + 30}{2} \\ z = \frac{84}{2} \\ z = 42 \end{matrix}$

Therefore, the values are $x = 8, y = 4, z = 42$ .

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Most popular questions from this chapter

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

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Prove: $∠ B ≅ ∠ E$

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