Q20 What values must x and y have to... [FREE SOLUTION]

91影视

Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q20 (page 175)

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

Short Answer

Expert verified

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

Step by step solution

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:

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

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:

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

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.

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91影视

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

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Find the value of x.

Step 3. Find the value of y.

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