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?