Chapter 4.2, Problem 13E

### 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

# In Exercises 11 to 14 , assume that X , Y , and Z are midpoints of the sides of ∆ R S T .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 âˆ†RST=20 units. X, Y, Z are the midpoints of the sides of âˆ†RST.

By the application of the â€˜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 sideâ€™, we have

XY=12RT,

YZ=12RS, and

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