Question

a triangle's base is 1/3 the height and the area is 6. find the base of the triangle

Answer 1

If base is one third the height, we can also say that the height is three times the base, or h=3B
Plugging this into the formula for the area of the triangle, we have:
A=½B×h
A=½(B)(3B)
A=(3/2)b²
We're told that the area is 6, so now you just need to solve:
6 = (3/2)B²