A cross between a tall and short plant is made. All of the offspring are intermediate height plants. These intermediate plants are self-fertilized, and the offspring have a broad distribution of heights. What can you conclude about genetic control of plant height?

Tall and short trees are genotypically homozygous for their trait

Intermediated trees are genotypically heterozygous for their trait.

Explanation:

Let the allele representing tall trait be "T"

and the allele representing short trait be "t"

It is given that when a  tall and short plant is fused all the offspring are of intermediate height.

This simply means that the both the plants are genotypically heterozygous for their traits

Genotype for tall tree - TT

Genotype for short tree - tt

TT * tt

Tt, Tt, Tt, Tt

All the offspring are of intermediate height.

Now these two plants of intermediate height are crossed

Tt * Tt

TT, Tt, Tt, tt

Out of four plants two are of intermediate height, one is of tall heingth and the remainig one is of short height