Question 261102
 a right triangle has hypotenuse of lenght 13 and legs A and B. If the area of the triangle is 14, what is the sum A+B? 
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a^2 + b^2 = 169
ab/2 = 14 --> a = 28/b
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(28/b)^2 + b^2 = 169
784 + b^4 = 169b^2
b^4 - 169b^2 + 784 = 0
Sub x for b^2
*[invoke solve_quadratic_equation 1,-169,784]
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b^2 =~ 164.226
b^2 =~ 4.7739
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b =~ 12.8166, a =~ 2.1849 or vice versa
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a + b = 15
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In any right triange with a specified lenght of the hypotenuse, the max area is
c^2/2.
For a hyp = 13, that's 169/2 = 84.5 sq units.  Any area less than that can be made with hyp = 13.