1953 AHSME Problems/Problem 41
Problem
A girls' camp is located rods from a straight road. On this road, a boys' camp is located rods from the girls' camp. It is desired to build a canteen on the road which shall be exactly the same distance from each camp. The distance of the canteen from each of the camps is:
Solution
Let be the straight road, be the girls' camp, be the boys' camp, and be the water canteen. is the perpendicular from to . Suppose each rod is one unit long. and . Since is a right angle, is a right triangle, so .
Let be the distance from the canteen to the girls' and boys' camps. We have and . Using the Pythagorean Theorem on , we have Simplifying the left side gives Subtracting from both sides and rearranging gives Therefore, . The answer is .
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 40 |
Followed by Problem 42 | |
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