`1225` plants are to be planted of rows. Find the number of rows and the number of plants in each row.

Options

A. `25`
B. `35`
C. `45`
D. `65`

Answer

To solve the problem of planting 1,225 plants in rows, we need to find a way to arrange these plants such that both the number of rows and the number of plants in each row are whole numbers.

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find two numbers, \( r \) (the number of rows) and \( p \) (the number of plants in each row), such that:
\[ r \times p = 1225 \]

2. **Finding Factors of 1225**: To find suitable values for \( r \) and \( p \), we need to find the factors of 1,225. This can be done by performing prime factorization.
- First, we divide 1,225 by 5 (the smallest prime number):
\[ 1225 \div 5 = 245 \]
- Next, we divide 245 by 5:
\[ 245 \div 5 = 49 \]
- Now, we factor 49, which is \( 7 \times 7 \).
- Therefore, the prime factorization of 1,225 is:
\[ 1225 = 5^2 \times 7^2 \]

3. **Calculating Factors**: From the prime factorization, we can find all the factors of 1,225:
- The factors of 1,225 are: 1, 5, 7, 25, 35, 49, 175, 245, and 1225.

4. **Finding Suitable Rows and Plants**: We can pair these factors to find possible combinations of rows and plants per row:
- \( (1, 1225) \)
- \( (5, 245) \)
- \( (7, 175) \)
- \( (25, 49) \)
- \( (35, 35) \)

5. **Choosing a Combination**: We can choose any of these combinations based on preference. For example, if we choose \( 35 \) rows, then:
\[ p = \frac{1225}{35} = 35 \]
This means we can have 35 rows with 35 plants in each row.

### Final Answer:
The number of rows is \( 35 \) and the number of plants in each row is \( 35 \).