The height of a plant is under the control of polygenic inheritance. The genotype of a plant `A_(1)A_(1)A_(0)A_(0)` has 56 cm and the height of plant `a_(1)a_(1)a_(0)a_(0)` is 26 cm. what is the contribution, of each polygene?

Options

A. 30 cm
B. 8.5 cm
C. 15 cm
D. 7.5 cm

Explanation

To solve the problem of determining the contribution of each polygene to the height of the plant, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Genotypes and Heights**:
- The genotype `A1A1A0A0` corresponds to a height of 56 cm.
- The genotype `a1a1a0a0` corresponds to a height of 26 cm.

2. **Calculate the Difference in Height**:
- Find the difference in height between the two genotypes:
\[ \text{Difference} = 56 \, \text{cm} - 26 \, \text{cm} = 30 \, \text{cm} \]

3. **Determine the Number of Contributing Genes**:
- Each genotype has 4 alleles (2 dominant and 2 recessive), meaning there are 4 genes contributing to the height.

4. **Calculate the Contribution of Each Polygene**:
- To find the contribution of each polygene, divide the difference in height by the number of genes:
\[ \text{Contribution per gene} = \frac{\text{Difference}}{\text{Number of genes}} = \frac{30 \, \text{cm}}{4} = 7.5 \, \text{cm} \]

5. **Conclusion**:
- The contribution of each polygene to the height of the plant is 7.5 cm.

### Final Answer:
The contribution of each polygene is **7.5 cm**.

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