Chapter 4.3, Problem 10E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 = x + y and BC = x + 2y, and CD = 2x – y – 1, and DA = 3x – 3y + 1 Find: x and y

To determine

To find:

x and y 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 = x + y and BC = x + 2y, and CD = 2x â€“ y â€“ 1, and DA = 3x â€“ 3y + 1

Consider the rectangle.

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

To find x and y:

From the property, opposite sides are congruent in rectangle.

So, AB = CD

x+y=2xâˆ’yâˆ’1â†’(1)

BC = DA

x+2y=3xâˆ’3y+1â†’(2)

Now we have to solve (1) and (2).

By solving (1), we get

x+y=2xâˆ’yâˆ’12xâˆ’x=y+y+1x=2y+1

By solving (2), we get

x+2y=3xâˆ’3y+

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