SOLUTION: the width, length, and diagonal of a rectangle are consecutive even integers. What are the integers.

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Question 355440: the width, length, and diagonal of a rectangle are consecutive even integers. What are the integers.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width of the rectangle, which is also the shortest side of the right triangle. Then the other leg is w +2, and w+4 is the hypotenuse. Then by the Pythagorean Theorem, w%5E2+%2B+%28w%2B2%29%5E2+=+%28w%2B4%29%5E2,
w%5E2%2B+w%5E2%2B4w%2B4+=+w%5E2+%2B8w%2B16,
w%5E2-4w-12+=+0,
%28w%2B2%29%28w-6%29+=+0.
Thus w = 6, and the other leg is 8, and the hypotenuse is 10.