the bases of a trapezoid are 10 and 12 and the nonparallel sides are 2 and 3. How far must each of the nonparallel sides be extended to form a triangle?
I don't think the figure described is a trapezoid.
Consider the figure as set up with the lower base drawn from (0,0) to (12,0)
Let the upper base go from (a,b) to (a+10,b)
Then we have two triangles at the sides such that
a^2 + b^2 = 4
a^2 + (2-a)^2 = 9
This gives a = -1/4, which means that both slanting sides lean to the left.
Have I missed something here?