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.
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 H2 = a2 + (4 * A2)/a2
On re-arranging, we get the equation a4 – (H2)(a2) + 4*(A2)
The discriminant D of this equation would be D = H4 – 16*(A2)
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)
3.0 4.0 5
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