   Chapter 4.1, Problem 9E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given that A B = 3 x + 2 , B C = 4 x + 1 , and C D = 5 x - 2 , find the length of each side of . To determine

To find:

The length of each side of ABCD.

Explanation

Given:

Given that AB=3x+2, BC=4x+1, and CD=5x-2, and the diagram as shown below.

Corollary:

The opposite sides of a parallelogram are congruent.

Calculation:

In the given parallelogram ABCD, given that AB=3x+2, BC=4x+1, and CD=5x-2.

As per the corollary that the opposite sides of a parallelogram are congruent, the opposite sides B=DC, and AD=BC.

Since AB=DC

3x+2=5x-2

3x-5x=-2-2

-2x=-4

x=-4-2=2

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