SOLUTION: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 3/4 length of the shorter side. If the dimensions of all sides are integers, find the minimum length
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Question 1100018: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 3/4 length of the shorter side. If the dimensions of all sides are integers, find the minimum length of the longer side.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
let x = shorter side
let y = longer side
The semiperimeter is then x+y; and then the length of the diagonal is
Then by the Pythagorean Theorem,
[note dividing by x is okay here, because we know the problem would make no sense if x were equal to 0]
The smallest solution in integers is y=15, x=8, making the diagonal 17.
The answer to the problem is the minimum length of the longer side, which is 15.
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