91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11, Problem 32RP

To determine

To calculate: The area ratio of region ⏸ and region ⏸.

Expert Solution

Answer to Problem 32RP

The area ratio is $5:4$ .

Explanation of Solution

Given information:

Side AC = 9,

Side BC = 6.

Formula used:

The below similar figures theorem is used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

Calculation:

Geometry For Enjoyment And Challenge, Chapter 11, Problem 32RP , additional homework tip 1

Triangle in region ⏸ is similar to triangle in region ⏸. These two triangles are similar to triangle in region ⏸ and ⏸.

$AⅠAⅡ=(s1s2)2AⅡAⅠ+AⅡ=(BCAC)2=(69)2=(23)2=49−−−−Equation 1AⅠAⅠ+AⅡ=99−49=59−−−−Equation 2$

Dividing Equation 1 by Equation 2, we get

$AⅠAⅡ=(5949)=54$

To determine

To find: The area ratio of region ⏸ and region ⏸.

Expert Solution

Answer to Problem 32RP

The area ratio is $25:39$ .

Explanation of Solution

Given information:

Side QS = 10,

Side SP = 6.

Formula used:

The below similar figures theorem is used:

Calculation:

Geometry For Enjoyment And Challenge, Chapter 11, Problem 32RP , additional homework tip 2

Triangle in region ⏸ is similar to triangle in region ⏸. These two triangles are similar to triangle in region ⏸ and ⏸.

$AⅠAⅠ+AⅡ=(QSQP)2=(58)2=2564−−−−Equation 1AⅡAⅠ+AⅡ=6464−2564=3964−−−−Equation 2$

Dividing Equation 1 by Equation 2, we get

$AⅠAⅡ=(25643964)=2539=25:39$

Chapter 11, Problem 31RP

Chapter 11, Problem 33RP

Chapter 11 Solutions

Geometry For Enjoyment And Challenge

Ch. 11.1 - Prob. 1PSA Ch. 11.1 - Prob. 2PSA Ch. 11.1 - Prob. 3PSA Ch. 11.1 - Prob. 4PSA Ch. 11.1 - Prob. 5PSA Ch. 11.1 - Prob. 6PSA Ch. 11.1 - Prob. 7PSA Ch. 11.1 - Prob. 8PSB Ch. 11.1 - Prob. 9PSB Ch. 11.1 - Prob. 10PSB

Ch. 11.1 - Prob. 11PSB Ch. 11.1 - Prob. 12PSB Ch. 11.1 - Prob. 13PSB Ch. 11.1 - Prob. 14PSB Ch. 11.1 - Prob. 15PSB Ch. 11.1 - Prob. 16PSC Ch. 11.1 - Prob. 17PSC Ch. 11.2 - Prob. 1PSA Ch. 11.2 - Prob. 2PSA Ch. 11.2 - Prob. 3PSA Ch. 11.2 - Prob. 4PSA Ch. 11.2 - Prob. 5PSA Ch. 11.2 - Prob. 6PSA Ch. 11.2 - Prob. 7PSA Ch. 11.2 - Prob. 8PSA Ch. 11.2 - Prob. 9PSA Ch. 11.2 - Prob. 10PSA Ch. 11.2 - Prob. 11PSA Ch. 11.2 - Prob. 12PSA Ch. 11.2 - Prob. 13PSB Ch. 11.2 - Prob. 14PSB Ch. 11.2 - Prob. 15PSB Ch. 11.2 - Prob. 16PSB Ch. 11.2 - Prob. 17PSB Ch. 11.2 - Prob. 18PSB Ch. 11.2 - Prob. 19PSB Ch. 11.2 - Prob. 20PSB Ch. 11.2 - Prob. 21PSB Ch. 11.2 - Prob. 22PSB Ch. 11.2 - Prob. 23PSB Ch. 11.2 - Prob. 24PSB Ch. 11.2 - Prob. 25PSB Ch. 11.2 - Prob. 26PSC Ch. 11.2 - Prob. 27PSC Ch. 11.2 - Prob. 28PSC Ch. 11.2 - Prob. 29PSC Ch. 11.2 - Prob. 30PSC Ch. 11.2 - Prob. 31PSC Ch. 11.2 - Prob. 32PSC Ch. 11.2 - Prob. 33PSC Ch. 11.3 - Prob. 1PSA Ch. 11.3 - Prob. 2PSA Ch. 11.3 - Prob. 3PSA Ch. 11.3 - Prob. 4PSA Ch. 11.3 - Prob. 5PSA Ch. 11.3 - Prob. 6PSA Ch. 11.3 - Prob. 7PSB Ch. 11.3 - Prob. 8PSB Ch. 11.3 - Prob. 9PSB Ch. 11.3 - Prob. 10PSB Ch. 11.3 - Prob. 11PSB Ch. 11.3 - Prob. 12PSB Ch. 11.3 - Prob. 13PSB Ch. 11.3 - Prob. 14PSC Ch. 11.3 - Prob. 15PSC Ch. 11.3 - Prob. 16PSC Ch. 11.3 - Prob. 17PSC Ch. 11.3 - Prob. 18PSC Ch. 11.3 - Prob. 19PSC Ch. 11.3 - Prob. 20PSC Ch. 11.4 - Prob. 1PSA Ch. 11.4 - Prob. 2PSA Ch. 11.4 - Prob. 3PSA Ch. 11.4 - Prob. 4PSB Ch. 11.4 - Prob. 5PSB Ch. 11.4 - Prob. 6PSB Ch. 11.4 - Prob. 7PSB Ch. 11.4 - Prob. 8PSB Ch. 11.4 - Prob. 9PSB Ch. 11.4 - Prob. 10PSC Ch. 11.4 - Prob. 11PSC Ch. 11.4 - Prob. 12PSC Ch. 11.4 - Prob. 13PSC Ch. 11.5 - Prob. 1PSA Ch. 11.5 - Prob. 2PSA Ch. 11.5 - Prob. 3PSA Ch. 11.5 - Prob. 4PSA Ch. 11.5 - Prob. 5PSA Ch. 11.5 - Prob. 6PSA Ch. 11.5 - Prob. 7PSA Ch. 11.5 - Prob. 8PSA Ch. 11.5 - Prob. 9PSA Ch. 11.5 - Prob. 10PSA Ch. 11.5 - Prob. 11PSA Ch. 11.5 - Prob. 12PSB Ch. 11.5 - Prob. 13PSB Ch. 11.5 - Prob. 14PSB Ch. 11.5 - Prob. 15PSB Ch. 11.5 - Prob. 16PSB Ch. 11.5 - Prob. 17PSB Ch. 11.5 - Prob. 18PSB Ch. 11.5 - Prob. 19PSC Ch. 11.5 - Prob. 20PSC Ch. 11.5 - Prob. 21PSC Ch. 11.5 - Prob. 22PSC Ch. 11.5 - Prob. 23PSC Ch. 11.5 - Prob. 24PSC Ch. 11.5 - Prob. 25PSC Ch. 11.5 - Prob. 26PSC Ch. 11.6 - Prob. 1PSA Ch. 11.6 - Prob. 2PSA Ch. 11.6 - Prob. 3PSA Ch. 11.6 - Prob. 4PSA Ch. 11.6 - Prob. 5PSA Ch. 11.6 - Prob. 6PSA Ch. 11.6 - Prob. 7PSA Ch. 11.6 - Prob. 8PSB Ch. 11.6 - Prob. 9PSB Ch. 11.6 - Prob. 10PSB Ch. 11.6 - Prob. 11PSB Ch. 11.6 - Prob. 12PSB Ch. 11.6 - Prob. 13PSB Ch. 11.6 - Prob. 14PSB Ch. 11.6 - Prob. 15PSB Ch. 11.6 - Prob. 16PSB Ch. 11.6 - Prob. 17PSB Ch. 11.6 - Prob. 18PSC Ch. 11.6 - Prob. 19PSC Ch. 11.6 - Prob. 20PSC Ch. 11.6 - Prob. 21PSC Ch. 11.6 - Prob. 22PSC Ch. 11.6 - Prob. 23PSC Ch. 11.7 - Prob. 1PSA Ch. 11.7 - Prob. 2PSA Ch. 11.7 - Prob. 3PSA Ch. 11.7 - Prob. 4PSA Ch. 11.7 - Prob. 5PSA Ch. 11.7 - Prob. 6PSA Ch. 11.7 - Prob. 7PSA Ch. 11.7 - Prob. 8PSA Ch. 11.7 - Prob. 9PSB Ch. 11.7 - Prob. 10PSB Ch. 11.7 - Prob. 11PSB Ch. 11.7 - Prob. 12PSB Ch. 11.7 - Prob. 13PSB Ch. 11.7 - Prob. 14PSB Ch. 11.7 - Prob. 15PSB Ch. 11.7 - Prob. 16PSB Ch. 11.7 - Prob. 17PSB Ch. 11.7 - Prob. 18PSC Ch. 11.7 - Prob. 19PSC Ch. 11.7 - Prob. 20PSC Ch. 11.7 - Prob. 21PSC Ch. 11.7 - Prob. 22PSC Ch. 11.8 - Prob. 1PSA Ch. 11.8 - Prob. 2PSA Ch. 11.8 - Prob. 3PSA Ch. 11.8 - Prob. 4PSB Ch. 11.8 - Prob. 5PSB Ch. 11.8 - Prob. 6PSB Ch. 11.8 - Prob. 7PSB Ch. 11.8 - Prob. 8PSB Ch. 11.8 - Prob. 9PSB Ch. 11.8 - Prob. 10PSB Ch. 11.8 - Prob. 11PSC Ch. 11.8 - Prob. 12PSC Ch. 11.8 - Prob. 13PSC Ch. 11 - Prob. 1RP Ch. 11 - Prob. 2RP Ch. 11 - Prob. 3RP Ch. 11 - Prob. 4RP Ch. 11 - Prob. 5RP Ch. 11 - Prob. 6RP Ch. 11 - Prob. 7RP Ch. 11 - Prob. 8RP Ch. 11 - Prob. 9RP Ch. 11 - Prob. 10RP Ch. 11 - Prob. 11RP Ch. 11 - Prob. 12RP Ch. 11 - Prob. 13RP Ch. 11 - Prob. 14RP Ch. 11 - Prob. 15RP Ch. 11 - Prob. 16RP Ch. 11 - Prob. 17RP Ch. 11 - Prob. 18RP Ch. 11 - Prob. 19RP Ch. 11 - Prob. 20RP Ch. 11 - Prob. 21RP Ch. 11 - Prob. 22RP Ch. 11 - Prob. 23RP Ch. 11 - Prob. 24RP Ch. 11 - Prob. 25RP Ch. 11 - Prob. 26RP Ch. 11 - Prob. 27RP Ch. 11 - Prob. 28RP Ch. 11 - Prob. 29RP Ch. 11 - Prob. 30RP Ch. 11 - Prob. 31RP Ch. 11 - Prob. 32RP Ch. 11 - Prob. 33RP Ch. 11 - Prob. 34RP Ch. 11 - Prob. 35RP Ch. 11 - Prob. 36RP Ch. 11 - Prob. 37RP Ch. 11 - Prob. 38RP Ch. 11 - Prob. 39RP Ch. 11 - Prob. 40RP Ch. 11 - Prob. 41RP Ch. 11 - Prob. 42RP Ch. 11 - Prob. 43RP Ch. 11 - Prob. 44RP Ch. 11 - Prob. 45RP

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