Diva 8v15 by 2v
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Let X and Y be the legs and Z be the hypotenuse.
X^2 + Y^2 = Z^2(equation 1)
1/2×X×Y = 6, Y = 12/X(equation 2)
X + Y + Z = 12, Z = 12 - (X + Y)(equation 3)
Substituting the second and third equation in first equation, we get
X^2 + (12/X)2 = (12 - (X + 12/X))^2
X^2 + 144/X^2 = (12 -(X^2 + 12)/X)^2
(X^4 + 144)/X^2 = ((12X -X^2 -12)/X)^2
(X^4 + 144)/X^2 = (12X - X^2 -12)^2/X^2
X^4 +144 = 144X^2 + X^4 + 144 -24X^3 -288X +24X^2
-24X^3 + 168X^2 -288X = 0
24X^3 -168X^2 + 288X = 0
X^3 - 7X^2 + 12X = 0, X(X^2 -7X +12) = 0
X×(X - 4)×(X - 3) = 0, X = 4, Y = 3
Using pythagoras theorem Z = 5
So the two legs of right triangle are 4 and 3, hypotenuse is 5.
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