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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