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Chapter 5: Q23 (page 170)

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 5 and 4 respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

In a given figure, by the property of a parallelogram,

2x+2y=18

02

Step 2. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

In a given figure, by the property of a parallelogram,

2x+5y=30

03

Step 3. Description of step.

Subtract the equation in step 1 from the equation in step 2.

2x+5y鈭�2x+2y=30鈭�182x+5y鈭�2x鈭�2y=123y=12y=4

04

Step 4. Description of step.

Substitute 4 for y into 2x+2y=18 to find the value of x.

2x+2脳4=182x+8=182x=10x=5

Therefore, the value of x and y is 5 and 4 respectively.

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