Given one side of right angle triangle, check if there exist a right angle triangle possible with any other two sides of the triangle. If possible print length of other two sides.
Else print -1
Note : All the sides of triangle must be positive integers
Input : a = 3 Output : b = 4, c = 5 Explanation : a = 3, b = 4 and c = 5 form right angle triangle because 32 + 42 = 9 + 16 = 25 = 52 => 32 + 42 = 52
Input : a = 11 Output : b = 60, c = 61 Explanation : a = 11, b = 60 and c = 61 form right angle triangle because 112 + 602 = 121 + 3600 = 3721 = 612 => 112 + 602 = 612
To solve this problem we first observe the Pythagoras equation. If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This relationship is represented by the formula:
a2 + b2 = c2
- Case 1 – a is an odd number: Given a, find b and c
c2 - b2 = a2 OR c = (a2 + 1)/2; b = (a2 - 1)/2;
Above solution works only for case when a is odd, because a2 + 1 is divisible by 2 only for odd a.
- Case 2 – a is an even number: When c-b is 2 & c+b is (a2)/2
c-b = 2 & c+b = (a2)/2 Hence, c = (a2)/4 + 1; b = (a2)/4 - 1;
This works when a is even.
This solution doesn’t work for case of a = 1 and a = 2 because there isn’t any right angle triangle with side 1 or 2 with all integer sides.
b = 4, c = 5
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Improved By : nitin mittal
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