Answer:
Assuming that tall plants are dominant and represented by the letter "T" and short plants are recessive and represented by the letter "t", the genotypes of the parents can be determined using the following cross:
TT or Tt (unknown) x tt (unknown)
From the 82 plants that were tall or short, we can assume that they were all heterozygous (Tt). Therefore, we can set up the following equation:
TT or Tt (unknown) x tt (unknown) = 82 Tt
To solve for the unknown genotypes, we can use Punnett squares or the formula:
(T + t) x (t + t) = Tt + Tt + tt + tt = 1Tt + 2tt
Where T represents the dominant allele and t represents the recessive allele. Since we know that 82 plants were Tt and that Tt represents two alleles, we can set up the equation:
1Tt + 2tt = 82 Tt
Simplifying the equation, we get:
2tt = 81 Tt
Dividing both sides by 2, we get:
tt = 40.5 Tt
Since we cannot have half an allele, we can assume that the parents were both heterozygous (Tt). Therefore, the genotypes of the parents in this cross must have been Tt x Tt.