#include<stdio.h>
#include<math.h>
int main()
{
    double a, b;
    printf("Enter the two perpendicular sides\n");
    
    printf("a: ");
    scanf("%lf", &a);
    
    printf("b: ");
    scanf("%lf", &b);
    
    printf("The area is %lf\n", 0.5*a*b);
    
    double hypotenuse = sqrt(a*a+b*b);
    printf("Hypotenuse: %lf\n", hypotenuse);
    
    /*
      Assuming equation of line as y=mx+c
      which passes through two points (0,b) and (a,0)
      we get:
             m = -b/a
             c = b
             
      Now, dist of point (0,0) from line is:
           b/sqrt(1+m^2)
    */
    
    double m = -b/a;
    double height = b/sqrt(1+m*m);
    
    printf("The area (using height) is %lf\n", 0.5*hypotenuse*height);
    
    if( 0.5*a*b == 0.5*hypotenuse*height )
        printf("Same");
    else
    {
        printf("Different");
        /*
          The areas may apppear equal, but they could be different at later digits.
          This can be seen by using the == operator.
          The reason is that real numbers of arbitrary precision cannot be 
          represented on a computer. So irrational numbers, often encountered 
          while using sqrt() will lose some precision. So when you calculate the area,
          the area (though appearing same) could be different.
          
          Test case: 5,12
        */
    }
    
}