   Chapter 8.1, Problem 31E ### 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

# For Exercise 31 and 32, X is the midpoint of V T ¯ and Y is the midpoint of T S ¯ . See the theorem in Exercise 30.If A R S T V = 48 cm 2 , find A R Y T X . Exercises 31, 32

To determine

To find:

ARYTX If ARSTV=48 cm2

Explanation

“A median of a triangle separated it into two triangles of equal area”.

Calculation:

Given,

Area of RSTV(A)=48 cm2

Draw a diagonal RT¯ in RSTV which separates RSTV into two triangle RVT and RVT

In RVT X is the midpoint of VT¯ from R

(i.e.) RX is the median of RVT since, “A median of a triangle separated it into two triangles of equal area”

(i.e.) RX¯ separates the RVT into RXV and RXT with equal area,

ARXV=ARXT

In RTS, Y is the midpoint of TS¯ from R.

(i.e.) RY¯ is the median of RTS

RY¯ separates the RTS into RYT and RYS with equal area,

ARYT=ARYS

Now, the figure becomes,

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