*ABC* and *DEF* are equilateral triangles of side
3 and 4 respectively. Construct an equilateral triangle whose area
is the sum of the area of *ABC* and *DEF* .

Does this work for any whole number side lengths?

If not, under what circumstances does it work?

What if the lengths of the sides of the triangles had been
*a* and *b* instead of 3 and 4, can you construct an
equilateral triangle whose area is the sum of the areas of
*ABC* and *DEF* ? What is the new area?