   Chapter 5.CR, Problem 33CR 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: A B C D ​ ​ ​       is     a     rectangle E is the midpoint of  B C ¯ A B = 16 , C F = 9 , A D = 24 Find: A E , E F , A F , m ∠ A E F To determine

To find:

AE, EF, AF, mAEF.

Explanation

Given:

Calculation:

From ΔBAE

Let us first take the triangle ΔABC

By Pythagoras theorem,

AE2=BA2+BE2AE2=162+122AE2=256+144AE2=400AE=400AE=20

To find EF, consider the triangle ΔECF

By Pythagoras theorem,

EF2=EC2+CF2EF2=122+92EF2=144+81EF2=225EF=225EF=15

By Pythagoras theorem,

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