   Chapter 5.3, Problem 39E 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

The distance across a pond is to be measured indirectly by using similar triangles .If X Y = 160 ft , Y W = 40 ft , T Y = 120 ft , and W Z = 50 ft , find X T . To determine

To find:

The distance across a pond XT by using the given information.

Explanation

Definition:

CSSTC:

Corresponding sides of similar triangles are proportional.

Description:

Given that the distance across a pond is to be measured by using similar triangles and if XY=160ft, YW=40ft, TY=120ft, and WZ=50ft.

The given figure is shown below.

Figure

From the given figure, it is observed that two triangles XYT and WYZ are similar. That is, ΔXYTΔWYZ.

From the definition of CSSTP, corresponding sides of similar triangles are proportional.

That is, WYYT=ZYYX=WZXT.

Consider first and last proportions WYYT=WZXT to find the distance of XT

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