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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

01

Step 1. Observe the given diagram.

The given diagram is:

02

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:

3x−40=x3x−x=402x=40x=402x=20

Therefore, the value of x is 20.

03

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:

y2=y+30y2−y−30=0y2−6y+5y−30=0yy−6+5y−6=0y−6y+5=0y=6,−5

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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Most popular questions from this chapter

Prove Theorem 5-1.

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