Geometry, Student Edition
Geometry, Student Edition
1st Edition
ISBN: 9780078884849
Author: McGraw-Hill, McGraw Hill
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 8.3, Problem 49HP
To determine

To calculate:

The perimeter of the triangle.

Expert Solution & Answer
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Answer to Problem 49HP

The perimeter of the triangle is 37.9 .

Explanation of Solution

Given information:

The ratio of the measure of the angles of a triangle is 1:2:3 and the length of the shortest side is 8 .

Calculation:

The expression a:b:c means that the ratio of the first two quantities is a:b , the ratio of the last two quantities is b:c , and the ratio of the first and last quantities a:c .

Just sum of the measures of the angles of a triangle is 180 .

Now solve for x

  1x+2x+3x=1806x=180(16)6x=(16)180x=30

Hence, the measures of the three angles are 1(30)=30,2(30)=60,3(30)=90

The triangle is a 30°60°90° triangle.

In a 30°60°90° triangle the length of the hypotenuse h is 2 times the length of the shorter leg s , and the length of the longer leg l is 3 times the length of the shorter leg.

  Geometry, Student Edition, Chapter 8.3, Problem 49HP

Theorem of 30°60°90° triangle shows that,

  h=2sx=2(8)x=16

And

  l=3sx=3(8)x=83

Find the perimeter of the triangle.

  P=8+83+16=24+8337.9

Hence, the perimeter of the triangle is 37.9 .

Chapter 8 Solutions

Geometry, Student Edition

Ch. 8.1 - Prob. 4CYUCh. 8.1 - Prob. 5CYUCh. 8.1 - Prob. 6CYUCh. 8.1 - Prob. 7CYUCh. 8.1 - Prob. 8PPSCh. 8.1 - Prob. 9PPSCh. 8.1 - Prob. 10PPSCh. 8.1 - Prob. 11PPSCh. 8.1 - Prob. 12PPSCh. 8.1 - Prob. 13PPSCh. 8.1 - Prob. 14PPSCh. 8.1 - Prob. 15PPSCh. 8.1 - Prob. 16PPSCh. 8.1 - Prob. 17PPSCh. 8.1 - Prob. 18PPSCh. 8.1 - Prob. 19PPSCh. 8.1 - Prob. 20PPSCh. 8.1 - Prob. 21PPSCh. 8.1 - Prob. 22PPSCh. 8.1 - Prob. 23PPSCh. 8.1 - Prob. 24PPSCh. 8.1 - Prob. 25PPSCh. 8.1 - Prob. 26PPSCh. 8.1 - Prob. 27PPSCh. 8.1 - Prob. 28PPSCh. 8.1 - Prob. 29PPSCh. 8.1 - Prob. 30PPSCh. 8.1 - Prob. 31PPSCh. 8.1 - Prob. 32PPSCh. 8.1 - Prob. 33PPSCh. 8.1 - Prob. 34PPSCh. 8.1 - Prob. 35PPSCh. 8.1 - Prob. 36PPSCh. 8.1 - Prob. 37PPSCh. 8.1 - Prob. 38PPSCh. 8.1 - Prob. 39PPSCh. 8.1 - Prob. 40PPSCh. 8.1 - Prob. 41PPSCh. 8.1 - Prob. 42PPSCh. 8.1 - Prob. 43PPSCh. 8.1 - Prob. 44PPSCh. 8.1 - Prob. 45PPSCh. 8.1 - Prob. 46PPSCh. 8.1 - Prob. 47PPSCh. 8.1 - Prob. 48PPSCh. 8.1 - Prob. 49HPCh. 8.1 - Prob. 50HPCh. 8.1 - Prob. 51HPCh. 8.1 - 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Prob. 6ACYPCh. 8.6 - Prob. 6BCYPCh. 8.6 - Prob. 1CYUCh. 8.6 - Prob. 2CYUCh. 8.6 - Prob. 3CYUCh. 8.6 - Prob. 4CYUCh. 8.6 - Prob. 5CYUCh. 8.6 - Prob. 6CYUCh. 8.6 - Prob. 7CYUCh. 8.6 - Prob. 8CYUCh. 8.6 - Prob. 9CYUCh. 8.6 - Prob. 10CYUCh. 8.6 - Prob. 11CYUCh. 8.6 - Prob. 12PPSCh. 8.6 - Prob. 13PPSCh. 8.6 - Prob. 14PPSCh. 8.6 - Prob. 15PPSCh. 8.6 - Prob. 16PPSCh. 8.6 - Prob. 17PPSCh. 8.6 - Prob. 18PPSCh. 8.6 - Prob. 19PPSCh. 8.6 - Prob. 20PPSCh. 8.6 - Prob. 21PPSCh. 8.6 - Prob. 22PPSCh. 8.6 - Prob. 23PPSCh. 8.6 - Prob. 24PPSCh. 8.6 - Prob. 25PPSCh. 8.6 - Prob. 26PPSCh. 8.6 - Prob. 27PPSCh. 8.6 - Prob. 28PPSCh. 8.6 - Prob. 29PPSCh. 8.6 - Prob. 30PPSCh. 8.6 - Prob. 31PPSCh. 8.6 - Prob. 32PPSCh. 8.6 - Prob. 33PPSCh. 8.6 - Prob. 34PPSCh. 8.6 - Prob. 35PPSCh. 8.6 - Prob. 36PPSCh. 8.6 - Prob. 37PPSCh. 8.6 - Prob. 38PPSCh. 8.6 - Prob. 39PPSCh. 8.6 - Prob. 40PPSCh. 8.6 - Prob. 41PPSCh. 8.6 - Prob. 42PPSCh. 8.6 - Prob. 43PPSCh. 8.6 - Prob. 44PPSCh. 8.6 - Prob. 45PPSCh. 8.6 - Prob. 46PPSCh. 8.6 - Prob. 47PPSCh. 8.6 - 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