   Chapter 5.2, Problem 40E 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

For Exercises 39 to 40, use intuition to from a proportion based on the drawing shown.A square with sides of length 2 in. rests (as shown) on a square with sides of length 6 in. Find the perimeter of trapezoid A B C D . To determine

To calculate:

The perimeter of trapezoid ABCD

Explanation

Given:

A square with sides of length 2in. rests on a square with sides of length 6in.

Definition Used:

If C is a point of XY¯ and XCY, then XC+CY=XY.

Square:

It is a four sides of regular polygon where all sides are equal and all the internal angle equal to 90.

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

Pythagoras Theorem:

It states that sum of the length of the two sides is equal to the square of the length of the hypotenuse (longest sides).

(Hypotenuse)2=(Base)2+(Perpendicular)2

Perimeter of Polygon:

It is the total distance around the outside of a polygon.

Calculation:

According to the segment-Addition Postulate, AB+BH=AH.

Let us assume that AB=x.

It is given that AHCDandAGFE is a square.

According to the property of a square, we can say that AH=HC=CD=DA=6in and AG=GF=FE=EA=2in.

Substitute the value of AHandAB in an equation AB+BH=AH, we get

x+BH=6BH=6x

By the condition of two similar polygon, EAHC=ABBH.

So,

26=x6x13=x6x6x=3x4x=6x=64x=32

So, AB=32

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