Given one side of right angle triangle, check if there exists a right angle triangle possible with any other two sides of the triangle. If possible print length of the 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
This article is contributed by Pratik Chhajer . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Find other two sides and angles of a right angle triangle
- Find the hypotenuse of a right angled triangle with given two sides
- Find area of triangle if two vectors of two adjacent sides are given
- Find all sides of a right angled triangle from given hypotenuse and area | Set 1
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Check whether triangle is valid or not if sides are given
- Area of a largest square fit in a right angle triangle
- Program to print binary right angle triangle
- Maximum number of squares that can fit in a right angle isosceles triangle
- Check whether right angled triangle is valid or not for large sides
- Probability of cutting a rope into three pieces such that the sides form a triangle
- Exterior angle of a cyclic quadrilateral when the opposite interior angle is given
- Angle between a chord and a tangent when angle in the alternate segment is given
- Find if it's possible to rotate the page by an angle or not.
- Find all possible triangles with XOR of sides zero