   Chapter 4.2, Problem 13E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 11 to 14 , assume that X , Y , and Z are midpoints of the sides of ∆ R S T .For Exercise 12 to 14, see the figure for Exercise 11.If the perimeter (sum of the lengths of all three sides) of ∆ R S T is 20, what is the perimeter of ∆ X Y Z ? To determine

To find:

The perimeter of the XYZ.

Explanation

Approach:

The line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one half the length of the third side.

Calculation:

Given,

The perimeter of RST=20 units. X, Y, Z are the midpoints of the sides of RST.

By the application of the ‘theorem the line segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to one half the length of the third side’, we have

XY=12RT,

YZ=12RS, and

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