SOLUTION: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 1/3 the length of the longer side. If the dimensions of all sides are integers, find the minimum len
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Question 1147941: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 1/3 the length of the longer side. If the dimensions of all sides are integers, find the minimum length of the shorter side.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
Let x be the length of the short side, and let y be the length of the long side.
The diagonal is then .
The problem says the diagonal is less than the semi-perimeter by 1/3 the length of the longer side; that is . So
y=0 would make no sense in the problem, so 5y-12x = 0. Then, if x and y are integers, x=5k and y=12k for some positive integer k. And since we are looking for the minimum length of the shorter side that satisfies the conditions, x=5 and y=12.
ANSWER: The minimum length of the shorter side is 5.
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