Given H (Hypotenuse) and A (area) of a right angled triangle, find the dimensions of right angled triangle such that the hypotenuse is of length H and its area is A. If no such triangle exists, print “Not Possible”.
Input : H = 10, A = 24 Output : P = 6.00, B = 8.00 Input : H = 13, A = 36 Output : Not Possible
Before moving to exact solution, let’s do some of mathematical calculations related to properties of Right angled triangle.
Suppose H = Hypotenuse, P = Perpendicular, B = Base and A = Area of right angled triangle.
We have some sort of equations as :
P^2 + B^2 = H^2 P * B = 2 * A (P+B)^2 = P^2 + B^2 + 2*P*B = H^2 + 4*A (P+B) = sqrt(H^2 + 4*A) ----1 (P-B)^2 = P^2 + B^2 - 2*P*B = H^2 - 4*A mod(P-B) = sqrt(H^2 - 4*A) ----2 from equation (2) we can conclude that if H^2 < 4*A then no solution is possible. Further from (1)+(2) and (1)-(2) we have : P = (sqrt(H^2 + 4*A) + sqrt(H^2 - 4*A) ) / 2 B = (sqrt(H^2 + 4*A) - sqrt(H^2 - 4*A) ) / 2
Below is the implementation of above approach:
P = 3.00 B = 4.00
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Improved By : vt_m