   Chapter 7.3, Problem 31E 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 regular octagon RSTUVWXY with each side of length 4, find the length of diagonal RU. (HINT: Extended sides, as shown, form a square.) To determine

To find:

The length of the diagonal RU.

Explanation

Consider the given figure.

Here, ABCD is a square with all vertex angles equal to 180°.

All four triangles are isosceles right triangle.

In triangle ASR, AS = AR

Use Pythagoras theorem in triangle ASR.

AR2+AS2=RS2AS2+AS2=422AS2=16AS2=8AS=22

In triangle DTU, DT = DU

Use Pythagoras theorem in triangle DTU.

DT2+DU2=TU2DT2+D

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