Given area and hypotenuse, the aim is to print all sides if right triangle can exist, else print -1. We need to print all sides in ascending order.

Examples:

Input : 6 5 Output : 3 4 5 Input : 10 6 Output : -1

We have discussed a solution of this problem in below post.

Find all sides of a right angled triangle from given hypotenuse and area | Set 1

In this post, a new solution with below logic is discussed.

Let the two unknown sides be a and b

Area : A = 0.5 * a * b

Hypotenuse Square : H^2 = a^2 + b^2

Substituting b, we get H^{2} = a^{2} + (4 * A^{2})/a^{2}

On re-arranging, we get the equation a^{4} – (H^{2})(a^{2}) + 4*(A^{2})

The discriminant D of this equation would be D = H^{4} – 16*(A^{2})

If D = 0, then roots are given by the linear equation formula, roots = (-b +- sqrt(D) )/2*a

these roots would be equal to the square of the sides, finding the square roots would give us the sides.

# Python program to check existence of # right triangle. from math import sqrt # Prints three sides of a right trianlge # from given area and hypotenuse if triangle # is possible, else prints -1. def findRightAngle(A, H): # Descriminant of the equation D = pow(H,4) - 16 * A * A if D >= 0: # applying the linear equation # formula to find both the roots root1 = (H * H + sqrt(D))/2 root2 = (H * H - sqrt(D))/2 a = sqrt(root1) b = sqrt(root2) if b >= a: print a, b, H else: print b, a, H else: print "-1" # Driver code # Area is 6 and hypotenuse is 5. findRightAngle(6, 5)

Output:

3.0 4.0 5

This article is contributed by **Harshit Agrawal**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.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.