   Chapter 5.2, Problem 25E 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

Pentagon A B C D E ∼ pentagon G H J K L (not shown), A B = 6 , and G H = 9. If the perimeter of A B C D E is 50 , find the perimeter of G H J K L .

To determine

To calculate:

The perimeter of the GHJKL.

Explanation

Given:

Pentagon ABCDE~ pentagon GHJKL.

AB=6 and GH=9.

Perimeter of the pentagon is 50.

Definition Used:

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.

Calculation:

First, we have to draw a pentagon ABCDE and GHJKL.

It is given that AB=6 and GH=9.

ABGH=69=23GH=32AB

According to the definition of similar polygons, ABGH=BCHJ=CDJK=DEKL=EALG.

So,

BCHJ=ABGH=23HJ=32BC

CDJK=ABGH=23JK=32CD

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