Chapter 5.3, Problem 39E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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, Î”XYTâˆ¼Î”WYZ.

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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