f equilateral triangle JKL is cut by three lines as shown above to form four equilateral triangles of equal area, what is the length of a side of one of the smaller triangles?

Answer 1

if we have similar triangles with sides in ration of r, then the areas are in the ratio of r^2.

Since each small triangle has 1/4 the area of the large triangle, its sides are 1/2 as big.