trig
posted by Inascent .
which ser of lenths will form a triangle with greater area? 6ft,8ft, 10ft or 6ft,8ft,12ft...

Two sides of a triangle with fixed lengths will give the largest area when they form a 90° angle, irrespective of the length of the third side.
Now use Pythagoras theorem to check if the given data fit in the above case.
Proof (it may be beyond what you are doing, but good for reference):
The area of a triangle with side lengths a and b, and included angle C is given by:
Area=a*b*sin(C)/2
and for given a and b, sin(C) is maximum when C=90°.