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Q20

Expert-verified

Geometry

Found in: Page 175

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

What values must x and y have to make the quadrilateral a parallelogram?

The values that must x and y must have to make the quadrilateral a parallelogram are 20 and 6 respectively.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Find the value of x.

As the diagonals of the parallelogram bisect each other.

Therefore, to make the given quadrilateral a parallelogram, the diagonals of the parallelogram must bisect each other.

Therefore, the value of x can be obtained as:

$\begin{matrix} 3 x - 40 = x \\ 3 x - x = 40 \\ 2 x = 40 \\ x = \frac{40}{2} \\ x = 20 \end{matrix}$

Therefore, the value of x is 20.

Step 3. Find the value of y.

As the diagonals of the parallelogram bisect each other.

Therefore, to make the given quadrilateral a parallelogram, the diagonals of the parallelogram must bisect each other.

Therefore, the value of y can be obtained as:

$\begin{matrix} y^{2} = y + 30 \\ y^{2} - y - 30 = 0 \\ y^{2} - 6 y + 5 y - 30 = 0 \\ y (y - 6) + 5 (y - 6) = 0 \\ (y - 6) (y + 5) = 0 \\ y = 6, - 5 \end{matrix}$

As the length of any side cannot be negative, therefore the only possible value of y is 6.

Therefore, the value of y is 6.

Most popular questions for Math Textbooks

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$A (3, 2), B (8, 2), C (?, ?), D (0, 5)$

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Theorem 5-5.

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