Question 1150663: In certain right triangles √h^2-a^2 = 24, where h represents the length of the hypotenuse and a is the length of one of the legs. Find all possible ordered pairs (h,a), where h, a ∈ N. Explain your reasoning thoroughly. By Spirit of Math.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Square both sides:
Factor the left hand side:
(1) Write 576 in every possible way as the product of two integers.
(2) For each of those ways, determine h and a.
(3) Reject solutions for which h and a are not both integers.
Note if h and a are to both be integers, then (h+a) and (h-a) must be either both even or both odd.
h+a h-a h a
-------------------
576 1 X X
288 2 145 143
192 3 X X
144 4 74 70
96 6 51 45
72 8 40 32
64 9 X X
48 12 30 18
36 16 26 10
32 18 25 7
Solutions:
(h,a) = {(145,143), (74,70), (51,45), (40,32), (30,18), (26,10), (25,7)}
Answer by ikleyn(52890)  (Show Source):
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