We can use a property of right angle triangle for solving this problem, which can be stated as follows,
A right angle triangle with fixed hypotenuse attains
maximum area, when it is isosceles i.e. both height
and base becomes equal so if hypotenuse if H, then
by pythagorean theorem,
Base2 + Height2 = H2
For maximum area both base and height should be equal,
b2 + b2 = H2
b = sqrt(H2/2)
Above is the length of base at which triangle attains
maximum area, given area must be less than this maximum
area, otherwise no such triangle will possible.
Now if given area is less than this maximum area, we can do a binary search for length of base, as increasing base will increases area, it is a monotonically increasing function where binary search can be applied easily. In below code, a method is written for getting area of right angle triangle, recall that for right angle triangle area is ½*base*height and height can be calculated from base and hypotenuse using pythagorean theorem. Below is the implementation of above approach:
// C++ program to get right angle triangle, given
// hypotenuse and area of triangle
// limit for float comparison
#define eps 1e-6
// Utility method to get area of right angle triangle,
Time complexity: O(log(n)) because using inbuilt sqrt function Auxiliary Space: O(1)
One more solution is discussed in below post. Check if right angles possible from given area and hypotenuse This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to email@example.com. 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.
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