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 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.
// C++ program to check existence of // right triangle. #include <bits/stdc++.h> using namespace std;
// Prints three sides of a right triangle // from given area and hypotenuse if triangle // is possible, else prints -1. void findRightAngle( int A, int H)
{ // Descriminant of the equation
long D = pow (H, 4) - 16 * A * A;
if (D >= 0)
{
// applying the linear equation
// formula to find both the roots
long root1 = (H * H + sqrt (D)) / 2;
long root2 = (H * H - sqrt (D)) / 2;
long a = sqrt (root1);
long b = sqrt (root2);
if (b >= a)
cout << a << " " << b << " " << H;
else
cout << b << " " << a << " " << H;
}
else
cout << "-1" ;
} // Driver code int main()
{ findRightAngle(6, 5);
} // This code is contributed By Anant Agarwal. |
// Java program to check existence of // right triangle. class GFG {
// Prints three sides of a right triangle
// from given area and hypotenuse if triangle
// is possible, else prints -1.
static void findRightAngle( double A, double H)
{
// Descriminant of the equation
double D = Math.pow(H, 4 ) - 16 * A * A;
if (D >= 0 )
{
// applying the linear equation
// formula to find both the roots
double root1 = (H * H + Math.sqrt(D)) / 2 ;
double root2 = (H * H - Math.sqrt(D)) / 2 ;
double a = Math.sqrt(root1);
double b = Math.sqrt(root2);
if (b >= a)
System.out.print(a + " " + b + " " + H);
else
System.out.print(b + " " + a + " " + H);
}
else
System.out.print( "-1" );
}
// Driver code
public static void main(String arg[])
{
findRightAngle( 6 , 5 );
}
} // This code is contributed by Anant Agarwal. |
# Python program to check existence of # right triangle. from math import sqrt
# Prints three sides of a right triangle # 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 = int (sqrt(root1))
b = int (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 )
|
// C# program to check existence of // right triangle. using System;
class GFG {
// Prints three sides of a right triangle
// from given area and hypotenuse if triangle
// is possible, else prints -1.
static void findRightAngle( double A, double H)
{
// Descriminant of the equation
double D = Math.Pow(H, 4) - 16 * A * A;
if (D >= 0) {
// applying the linear equation
// formula to find both the roots
double root1 = (H * H + Math.Sqrt(D)) / 2;
double root2 = (H * H - Math.Sqrt(D)) / 2;
double a = Math.Sqrt(root1);
double b = Math.Sqrt(root2);
if (b >= a)
Console.WriteLine(a + " " + b + " " + H);
else
Console.WriteLine(b + " " + a + " " + H);
}
else
Console.WriteLine( "-1" );
}
// Driver code
public static void Main()
{
findRightAngle(6, 5);
}
} // This code is contributed by vt_m. |
<?php // PHP program to check existence of // right triangle. // Prints three sides of a right triangle // from given area and hypotenuse if // triangle is possible, else prints -1. function 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 )
echo $a , " " , $b , " " , $H ;
else
echo $b , " " , $a , " " , $H ;
}
else
echo "-1" ;
} // Driver code
findRightAngle(6, 5);
// This code is contributed By Anuj_67 ?> |
<script> // Javascript program to check existence of // right triangle. // Prints three sides of a right triangle // from given area and hypotenuse if triangle // is possible, else prints -1. function findRightAngle(A,H)
{ // Descriminant of the equation
let D = Math.pow(H, 4) - 16 * A * A;
if (D >= 0)
{
// applying the linear equation
// formula to find both the roots
let root1 = (H * H + Math.sqrt(D)) / 2;
let root2 = (H * H - Math.sqrt(D)) / 2;
let a = Math.sqrt(root1);
let b = Math.sqrt(root2);
if (b >= a)
document.write(a + " " + b + " " + H+ "<br/>" );
else
document.write(b + " " + a + " " + H+ "<br/>" );
}
else
document.write( "-1" );
} // Driver code findRightAngle(6, 5);
// This code contributed by Rajput-Ji </script> |
Output:
3 4 5
Time complexity: O(log(n)) since using inbuilt sqrt functions
Auxiliary Space: O(1)