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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 7.2, Problem 27E
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Elementary Geometry for College St...

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

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Given: Isosceles Δ R S T R S = R T = 17         a n d         S T = 16. Medians R Z ¯ , T X ¯ and S Y ¯ meet at centroid Q .

Find: R Q         and           S Q

Chapter 7.2, Problem 27E, Given: Isosceles RST RS=RT=17andST=16. Medians RZ, TX and SY meet at centroid Q. Find: RQandSQ

Exercises 29, 30

To determine

To find:

The RQ and SQ in the given isosceles triangle RST.

Explanation

Definition:

The three medians of a triangle are congruent at a point that is two-thirds the distance from any vertex to the midpoint of the opposite side.

Formula used:

The triangle RST, with sides a,b and c opposite vertices R,S and T. Then the length of the median ma form R is given by

ma=122(b2+c2)−a2

The length of the median mb form S is given by

mb=122(c2+a2)−b2

Where ma,mb denotes the length of the median

Given:

In ΔRST, medians RZ¯, TX¯ and SY¯ intersect at centroid Q. If RS=RT=17 and ST=16.

Calculation:

The point of concurrence Q for the three medians of a triangle is known as centroid of the triangle. In ΔMNP, medians MB¯, NA¯ and PC¯ intersect at centroid Q.

According to the definition,

RQ=23(RZ)                                    ⋅⋅⋅(1)SQ=23(SY)                                    ⋅⋅⋅(2)

Given RS=RT=17 and ST=16.

The triangle RST, with sides a,b and c opposite vertices R,S and T.

So, ST=16=a, RT=17=b and RS=17=c .

We sketch the figure of the isosceles triangle RST with sides a,b and c

First we need to find length of the median RZ,

Using the above formula,

The length of the median ma form R is given by

RZ=ma=122(b2+c2)−a2                                          =122(172+172)−162                                          =122(289+289)−256                                          =122(578)−256                                          =121156−256                                        =12900                 

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Sect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10E
Sect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.1 P-45ESect-7.1 P-46ESect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-29ESect-7.2 P-30ESect-7.2 P-31ESect-7.2 P-32ESect-7.2 P-33ESect-7.2 P-34ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.3 P-33ESect-7.3 P-34ESect-7.3 P-35ESect-7.3 P-36ESect-7.CR P-1CRSect-7.CR P-2CRSect-7.CR P-3CRSect-7.CR P-4CRSect-7.CR P-5CRSect-7.CR P-6CRSect-7.CR P-7CRSect-7.CR P-8CRSect-7.CR P-9CRSect-7.CR P-10CRSect-7.CR P-11CRSect-7.CR P-12CRSect-7.CR P-13CRSect-7.CR P-14CRSect-7.CR P-15CRSect-7.CR P-16CRSect-7.CR P-17CRSect-7.CR P-18CRSect-7.CR P-19CRSect-7.CR P-20CRSect-7.CR P-21CRSect-7.CR P-22CRSect-7.CR P-23CRSect-7.CR P-24CRSect-7.CR P-25CRSect-7.CR P-26CRSect-7.CR P-27CRSect-7.CR P-28CRSect-7.CR P-29CRSect-7.CR P-30CRSect-7.CR P-31CRSect-7.CR P-32CRSect-7.CR P-33CRSect-7.CR P-34CRSect-7.CT P-1CTSect-7.CT P-2CTSect-7.CT P-3CTSect-7.CT P-4CTSect-7.CT P-5CTSect-7.CT P-6CTSect-7.CT P-7CTSect-7.CT P-8CTSect-7.CT P-9CTSect-7.CT P-10CTSect-7.CT P-11CTSect-7.CT P-12CTSect-7.CT P-13CTSect-7.CT P-14CTSect-7.CT P-15CTSect-7.CT P-16CTSect-7.CT P-17CT

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