The length and breadth of a rectangular field are in the ratio of `3:2` .if the perimeter of the field is 80 cm ,its breadth (in metres) is:

Options

A. 18
B. 16
C. 10
D. 24

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the ratio of length and breadth
The length (L) and breadth (B) of the rectangular field are given in the ratio of 3:2. This means we can express them in terms of a variable \( x \):
- Length \( L = 3x \)
- Breadth \( B = 2x \)

**Hint:** Ratios can be expressed using a common variable to simplify calculations.

### Step 2: Use the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2(L + B) \]
We know the perimeter is 80 cm, so we can set up the equation:
\[ 80 = 2(L + B) \]

**Hint:** Remember that the perimeter is the total distance around the rectangle.

### Step 3: Substitute the expressions for length and breadth into the perimeter formula
Substituting \( L \) and \( B \) into the perimeter formula gives:
\[ 80 = 2(3x + 2x) \]

**Hint:** Combine like terms inside the parentheses to simplify the equation.

### Step 4: Simplify the equation
Now simplify the equation:
\[ 80 = 2(5x) \]
\[ 80 = 10x \]

**Hint:** When you multiply, ensure to distribute correctly.

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 10:
\[ x = \frac{80}{10} \]
\[ x = 8 \]

**Hint:** Dividing both sides by the same number helps isolate the variable.

### Step 6: Find the breadth
Now that we have \( x \), we can find the breadth:
\[ B = 2x = 2 \times 8 = 16 \text{ cm} \]

**Hint:** Always substitute back into the original expressions to find the desired quantity.

### Step 7: Convert breadth to meters
Since the question asks for the breadth in meters, we need to convert centimeters to meters:
\[ 16 \text{ cm} = \frac{16}{100} \text{ m} = 0.16 \text{ m} \]

**Hint:** Remember that 1 meter = 100 centimeters when converting units.

### Final Answer:
The breadth of the rectangular field is **0.16 meters**.