math
posted by Blonde Glamour .
consider the right traingel with sices 3, 4, and 5. the lengths form an arithmetic series.
a. what are the other three right triangles in arthimetic series
Actually, I think there are an infinite numbr of such triangles.
You want to have sides a, b and c such that a < b < c and b  a = c  b.
This means that:
c = 2 b  a
You also know that:
c^2 = a^2 + b^2 >
c^2  b^2 = a^2
(cb)(c+b) = a^2
(ba)(3ba) = a^2 >
3 b^2  4ba = 0 >
3b  4a = 0 >
b = 4/3 a
E.g.
take a = 27, then b = 36 and c should be 36 plus the difference of 36 and 27, which is 45. Pythagoras gives
c = sqrt[27^2 + 36^2] which is indeed 45.
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