   Chapter 4.2, Problem 29E 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

In Exercises 29 to 31, M and N are the midpoints of sides R S ¯ and R T ¯ of ∆ R S T , respectively. Given: M N = 2 y - 3 S T = 3 y Find: y , M N , and S T To determine

To find:

y, MN, and ST.

For MN=2y-3

ST=3y

Explanation

Calculation:

Given,

MN=2y-3

ST=3y

M N are the midpoints of sides RS¯ and RT¯ of RST respectively.

A 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.

Thus,

MN=12ST

2y-3=12(3y)

Multiply; by 2 on both sides,

22y-2=2·12(3y)

22y-2=3y

Apply, the distributive property of multiplication over subtraction to the left of the equation

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