The longest side of a polygon exceeds twice the length of the longest side of a similar polygon by 3. if the ratio of similitude of the polygons is 4: 9, find the length of the longest side of each polygon.

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

Uneed to add them up 27+18+23=68