2012 AMC 10B Problems/Problem 12
Problem
Point is due east of point . Point is due north of point . The distance between points and is , and . Point is meters due north of point . The distance is between which two integers?
Solution
If point B is due east of point A and point C is due north of point B, is a right angle. And if , is a 45-45-90 triangle. Thus, the lengths of sides , , and are in the ratio , and is .
is clearly a right triangle with on the side . is 20, so .
By the Pythagorean Theorem, .
, and . Thus, must be between and . The answer is .
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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