Problem:
The three sides of a right triangle have integral lengths which form an arithmetic progression. One of the sides could have length
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the sides of the triangle have lengths . Then by the Pythagorean theorem
Squaring and rearranging the terms yields
Since must be positive, . Thus the sides have lengths . Since the sides must have lengths divisible by or , only choice (C) could be the length of a side.