A total of 1152 students were assembled in rows and colums. If there are n rows and n/2 columns,then find the number of students in each row.

Options

A. 36
B. 42
C. 48
D. 34

Answer

To solve the problem step by step, we need to determine how many students are in each row given that there are \( n \) rows and \( \frac{n}{2} \) columns, and the total number of students is 1152.

### Step 1: Set up the equation
We know that the total number of students can be calculated by multiplying the number of rows by the number of columns. Thus, we can write the equation as:
\[ \text{Total Students} = \text{Number of Rows} \times \text{Number of Columns} \]
Substituting the values we have:
\[ 1152 = n \times \frac{n}{2} \]

### Step 2: Simplify the equation
We can simplify the equation:
\[ 1152 = \frac{n^2}{2} \]
To eliminate the fraction, multiply both sides by 2:
\[ 2304 = n^2 \]

### Step 3: Solve for \( n \)
Now, we take the square root of both sides to find \( n \):
\[ n = \sqrt{2304} \]

### Step 4: Calculate \( n \)
Calculating the square root:
\[ n = 48 \]

### Step 5: Find the number of columns
Now that we have \( n \), we can find the number of columns:
\[ \text{Number of Columns} = \frac{n}{2} = \frac{48}{2} = 24 \]

### Step 6: Find the number of students in each row
Finally, to find the number of students in each row, we can use the number of columns:
\[ \text{Number of Students in Each Row} = \text{Number of Columns} = 24 \]

### Final Answer
Thus, the number of students in each row is:
\[ \boxed{24} \]