The length and breadth of a rectangular field are in the ratio of 5:2. If the perimeter of the field is 140 metres, then what is the breadth (in metres) ?

Options

A. 20
B. 25
C. 30
D. 35

Answer

To find the breadth of the rectangular field, we can follow these steps:

### Step 1: Understand the Ratio
The length (L) and breadth (B) of the rectangular field are in the ratio of 5:2. This means we can express them as:
- Length, L = 5x
- Breadth, B = 2x
where x is a common multiplier.

### Step 2: Use the Perimeter Formula
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
Substituting the expressions for L and B, we have:
\[ P = 2(5x + 2x) \]
\[ P = 2(7x) \]
\[ P = 14x \]

### Step 3: Set the Perimeter Equal to the Given Value
We know from the problem that the perimeter is 140 meters. Therefore, we can set up the equation:
\[ 14x = 140 \]

### Step 4: Solve for x
To find the value of x, divide both sides of the equation by 14:
\[ x = \frac{140}{14} \]
\[ x = 10 \]

### Step 5: Calculate the Breadth
Now that we have the value of x, we can find the breadth (B):
\[ B = 2x \]
Substituting the value of x:
\[ B = 2 \times 10 \]
\[ B = 20 \]

### Conclusion
The breadth of the rectangular field is **20 meters**.

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