1953 AHSME Problems/Problem 46
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Problem 46
Instead of walking along two adjacent sides of a rectangular field, a boy took a shortcut along the diagonal of the field and
saved a distance equal to the longer side. The ratio of the shorter side of the rectangle to the longer side was:
Solution
Let be the sides of the rectangle. The length of the diagonal is
, and the length of the two adjacent sides is
. Then the distance the boy saves is
. Setting this equal to
, we have
so the answer is
.