Let
length of the longest side of the SMALLER polygon = x
then
length of the longest side of the LARGER polygon = 2x+3
We are given the ratio of similitude is 4:9, which is also the ratio of the sides.
So we equate the ratios and solve for x

Cross multiply:

expand by distributing 4 (to both terms in parentheses)

subtract 8x from both sides


Hence the
longest side of smaller polygon = x = 12 units
longest side of larger polygon = 2x+3 = 2*12+3 = 27 units