Two triangles have the same heights. One triangle has a base length that is twice the base length of the other triangle. Are the base lengths and the areas of the two triangles proportional?

Yes

Step-by-step explanation:

The formula for area of a triangle is A = (1/2) bh,

For the first triangle we can leave it in general terms, so it's area is

A = (1/2) bh, depending on what b and h are, but it doesn't matter here ...

The second triangle has base that is twice the other triangles base. Bases being multiples of each other is the definition of being proportional so the bases are proportional, an the area of the second triangle is

A = (1/2) (2b) h, which simplifies to

A = bh

Comparing the 2 areas, you can see that one has a multiplier of (1/2), so their areas are proportional