   Chapter 4.3, 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

In Exercises 8 to 10, use the properties of rectangles to solve each problem. Rectangle ABCD is shown in the figure. Exercises 8 - 10 Given: AB = 2x + 7 and BC = 3x + 4, and CD = 3x + 2 Find: x and DA

To determine

To find:

x and DA of the given rectangle.

Explanation

The basic property of rectangle:

1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).

2) All angles are right angles by definition.

3) The diagonals are congruent.

Calculation:

Given: AB = 2x + 7 and BC = 3x + 4, and CD = 3x + 2

Consider the rectangle.

Now we have to find x and DA of the given rectangle.

To find x:

From the property, opposite sides are congruent in rectangle.

So, AB = CD

2x+7=3x+23x

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