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

Options

A. a.18
B. b.16
C. c.10
D. d.24

Answer

To solve the problem, we need to find the breadth of a rectangular field given the ratio of its length and breadth and its perimeter. Here’s a step-by-step solution:

### Step 1: Understand the ratio of length and breadth
The length (L) and breadth (B) of the rectangular field are in the ratio of 3:2. We can express this as:
- Length = 3x
- Breadth = 2x
where x is a common multiplier.

### Step 2: Write the formula for the perimeter of a rectangle
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times (L + B) \]

### Step 3: Substitute the values into the perimeter formula
Given that the perimeter is 80 meters, we can substitute the expressions for length and breadth into the perimeter formula:
\[ 80 = 2 \times (3x + 2x) \]

### Step 4: Simplify the equation
Combine the terms inside the parentheses:
\[ 80 = 2 \times (5x) \]
This simplifies to:
\[ 80 = 10x \]

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

### Step 6: Calculate the length and breadth
Now that we have the value of x, we can find the length and breadth:
- Length (L) = 3x = 3 × 8 = 24 meters
- Breadth (B) = 2x = 2 × 8 = 16 meters

### Step 7: State the final answer
The breadth of the rectangular field is 16 meters.

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