Difference between revisions of "1973 AHSME Problems/Problem 20"
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| + | ==Problem== | ||
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| + | A cowboy is 4 miles south of a stream which flows due east. He is also 8 miles west and 7 miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this is | ||
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| + | <math> \textbf{(A)}\ 4+\sqrt{185} \qquad | ||
| + | \textbf{(B)}\ 16 \qquad | ||
| + | \textbf{(C)}\ 17 \qquad | ||
| + | \textbf{(D)}\ 18 \qquad | ||
| + | \textbf{(E)}\ \sqrt{32}+\sqrt{137}</math> | ||
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| + | ==Solution== | ||
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First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a <math>8, 15, 17</math> Pythagorean triple, so the answer is <math>17</math>, which is <math>\boxed{C}</math>. | First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a <math>8, 15, 17</math> Pythagorean triple, so the answer is <math>17</math>, which is <math>\boxed{C}</math>. | ||
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| + | ==See Also== | ||
{{AHSME 35p box|year=1973|before=[[1972 AHSME]]|after=[[1974 AHSME]]}} | {{AHSME 35p box|year=1973|before=[[1972 AHSME]]|after=[[1974 AHSME]]}} | ||
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| + | [[Category:Introductory Geometry Problems]] | ||
Revision as of 11:18, 5 July 2018
Problem
A cowboy is 4 miles south of a stream which flows due east. He is also 8 miles west and 7 miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this is
Solution
First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a 
Pythagorean triple, so the answer is 
, which is 
.
See Also
| 1973 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by 1972 AHSME |
Followed by 1974 AHSME | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
