SOLUTION: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 3/4 the length of the shorter side. If the dimensions of all sides are integers, find the minimum le

Question 1187047: The length of the diagonal of a rectangle is shorter than the semi-perimeter by 3/4 the length of the shorter side. If the dimensions of all sides are integers, find the minimum length of the longer side.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let x be the length of the longer side
Let y be the length of the shorter side

The length of the diagonal is

The length is also equal to the semiperimeter minus 3/4 the length of the shorter side:

So

or

y=0 makes no sense in the problem, so 15y-8x=0.

With the requirement that x and y be integers, the smallest solution is with x=15 and y=8.

ANSWER: The minimum length of the longer side is x=15.

CHECK:

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