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Q20

Expert-verifiedFound in: Page 175

Book edition
Student Edition

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

Pages
227 pages

ISBN
9780395977279

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.

The given diagram is:

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:

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

Therefore, the value of *x* is 20.

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:

$\begin{array}{c}{y}^{2}=y+30\\ {y}^{2}-y-30=0\\ {y}^{2}-6y+5y-30=0\\ y\left(y-6\right)+5\left(y-6\right)=0\\ \left(y-6\right)\left(y+5\right)=0\\ y=6,-5\end{array}$

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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