There is certain number of rows of chairs in a room .The number of chairs in each row is thrice the total number of rows. Find the number of charis in each row and number of rows in the room if the total number of chairs is 2187

Answer

To solve the problem, we need to find the number of rows of chairs and the number of chairs in each row given that the total number of chairs is 2187.

Let's break down the problem step by step:

### Step 1: Define the variables
Let the number of rows be \( x \). According to the problem, the number of chairs in each row is thrice the total number of rows. Therefore, the number of chairs in each row can be expressed as \( 3x \).

### Step 2: Write the equation for total chairs
The total number of chairs can be calculated by multiplying the number of rows by the number of chairs in each row. Thus, we can write the equation:
\[ \text{Total chairs} = \text{Number of rows} \times \text{Number of chairs in each row} \]
Substituting the values we have:
\[ 2187 = x \times 3x \]

### Step 3: Simplify the equation
This simplifies to:
\[ 2187 = 3x^2 \]

### Step 4: Solve for \( x^2 \)
To isolate \( x^2 \), divide both sides by 3:
\[ x^2 = \frac{2187}{3} \]
Calculating the right side:
\[ x^2 = 729 \]

### Step 5: Take the square root
To find \( x \), take the square root of both sides:
\[ x = \sqrt{729} \]
Calculating the square root:
\[ x = 27 \]

### Step 6: Find the number of chairs in each row
Now that we have \( x \), we can find the number of chairs in each row:
\[ \text{Number of chairs in each row} = 3x = 3 \times 27 = 81 \]

### Final Answer
- Number of rows: \( 27 \)
- Number of chairs in each row: \( 81 \)