How can you tell if three positive numbers form a pythagorean triple?

Which is a true statement comparing the graphs of x^2/6^2-y^2/8^2 = 1 and x^2/8^2-y^2/6^2 the foci of both graphs are the same points. the lengths of both transverse axes are the same. the directrices of = 1 are horizontal while the directrices of = 1 are vertical. the vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

How to do this , and can some one explain

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.