True-breeding strains

You are studying a species of plants that has a wide geographic distribution, and have identified two true-breeding strains, both of which produce plants that are 24 cm in height.  One strain came from Central America and the second from West Central Africa.  You cross the two strains and the F1 progeny are 24 cm in height.  However, when you allow the F1s to self fertilize, the heights of the F2 progeny range from 12 cm to 36 cm. a. What mode of inheritance is occurring?b. Among the F2 progeny you find that approximately 1/250 are 12 cm and ~1/250 are 36 cm tall.  How many genes are involved in regulating height in this species? c. What are the probable genotypes of the true-breeding parents and the F1 progeny?d. How much does each additive allele contribute to the height of the plant? e. What would you predict is/are the genotype(s) of members of this species that are 18 cm tall?Hello Mode of inheritance is polygenic InheritanceI know my parents are going to be AAbbCCdd X aaBBccDDMy F1 is AaBbCcDd36-12 = 24 cm24 / 8 alleles = 3 cm per additive contributed18 cm tall so 2 additive alleles. (12+3+3 = 18 cm)I am confused on the Genotype portion. Am I suppose to do a binomial expansion???