Have you been learning about the Pythagorean theorem? That's how to
solve this problem.
Remember that it says that a2 + b2 = c2, where c is the length of
the hypotenuse of a right triangle and a and b are the lengths of the
"legs" (the other two sides). What you are describing is a right
triangle, and the slant is the hypotenuse. So c = 6.
Now it sounds like you don't know a or b, so one equation isn't going
to be enough to solve the problem. But actually there is a second
equation given by the question: 2a = b, because the base is twice the
height. That means you can substitute 2a in for b in the Pythagorean
formula and you get this: a2 + (2a)2 = 62.
Now you should be able to solve the rest of the problem.
Hope this helps,
Stephen La Rocque.
P.S.: I'm not sure why you said "equilateral triangle", because that's
not implied by the question. If that's a separate question, you'll
need to send it to us separately.
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.