Question 893546
Is x a positive number?  If it is, then the longest side (hyptenuse) is either 60 units or x+12 units.
Use the Pythagorean Theorem both ways and solve each of them for x.


Hypotenuse 60:
{{{x^2+(x+12)^2=60^2}}}
{{{x^2+x^2+24x+144=3600}}}
{{{2x^2+24x-3600+144=0}}}
{{{x^2+12x-1728=0}}}
Discriminant, {{{highlight_green(144+4*1728=7056=84^2)}}}
{{{x=(-12+84)/2}}}
{{{highlight(x=36)}}}
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Shortest leg is 36, next leg is 48, and the 60 is hypotenuse.


You could try this again assuming x+12 is the hypotenuse, set up the Pythagorean Theorem
relationship, and see what happens, or if the solution works right.