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Chapter 5: Q21 (page 175)

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

Short Answer

Expert verified

The values that x and y must have to make the quadrilateral a parallelogram are 10 and 2 respectively.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

In a parallelogram, both pairs of opposite sides are congruent.

Therefore, to make the given quadrilateral a parallelogram, the pairs of opposite sides are congruent.

Therefore, it can be obtained as:

4x+y=4213x−2y=262

From the equation, it can be obtained as:

4x+y=42y=42−4x

03

Step 3. Find the value of x.

Now, substitute the value of y in equation (2) to find the value of x.

Therefore, the value of x can be obtained as:

3x−242−4x=263x−84+8x=2611x−84=2611x=26+8411x=110x=11011x=10

Therefore, the value of x is 10.

04

Step 4. Find the value of y.

Now, substitute 10 for x in the equation y=42−4xto find the value of y.

Therefore, the value of y can be obtained as:

y=42−410=42−40=2

Therefore, the value of y is 2.

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Most popular questions from this chapter

Parallel rulers, used to draw parallel lines, are constructed so that EF=HGand HE=GF. Since there are hinges at points E, F, G and H, you can vary the distance between role="math" localid="1637730770232" HG↔and role="math" localid="1637730792914" EF↔. Explain why HG↔and EF↔are always parallel.

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