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
[tex]\frac{x}{2x+3}=\frac{4}{9}[/tex]
Cross multiply:
[tex]9x=4(2x+3)[/tex]
expand by distributing 4 (to both terms in parentheses)
[tex]9x=8x+12)[/tex]
subtract 8x from both sides
[tex]9x-8x=12)[/tex]
[tex]x=12)[/tex]
Hence the
longest side of smaller polygon = x = 12 units
longest side of larger polygon = 2x+3 = 2*12+3 = 27 units
