Pre-Calculus Homework Solutions 140

# Pre-Calculus Homework Solutions 140 - 50 Sample answer The...

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50. Sample answer: The length of any side of a triangle is greater than the differences between the lengths of the other two sides. Paragraph Proof: By the Triangle Inequality Theorem, for ABC with side measures a , b , and c , a b c , b c a , and c a b . Using the Subtraction Property of Inequality, a c b , b a c , and c b a . 51. Sample answer: You can use the Triangle Inequality Theorem to verify the shortest route between two locations. Answers should include the following. • A longer route might be better if you want to collect frequent flier miles. • A straight route might not always be available. 52. D; If the perimeter is 29, the measure of the third side is 10. 7 10 ¬ ? 12 7 12 ¬ ? 10 10 12 ¬ ? 7 17 ¬ 12 19 ¬ 10 22 ¬ 7 So, 7, 12, and 10 could be the sides of a triangle with perimeter 29. If the perimeter is 34, the measure of the third side is 15. 7 15 ¬ ? 12 7 12 ¬ ? 15 12 15 ¬ ? 7 22 ¬ 12 19 ¬ 15 27 ¬ 7 So, 7, 12, and 15 could be the sides of a triangle with perimeter 34.
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