The length and breadth of a rectangular field are in the ratio of 4 : 3. If the perimeter of the field is 70 m, then what will be the breadth (in metres)?

Options

A. 12
B. 15
C. 18
D. 24

Answer

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

### Step 1: Understand the Ratio
The length (L) and breadth (B) of the rectangular field are in the ratio of 4:3. This means we can express the length and breadth in terms of a variable. Let:
- Length (L) = 4x
- Breadth (B) = 3x

**Hint:** When given a ratio, express the quantities in terms of a common variable.

### Step 2: Use the Perimeter Formula
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
We know the perimeter is 70 meters, so we can set up the equation:
\[ 70 = 2(4x + 3x) \]

**Hint:** Remember the formula for the perimeter of a rectangle and substitute the expressions for length and breadth.

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ 70 = 2(7x) \]
\[ 70 = 14x \]

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

### Step 4: Solve for x
Now, divide both sides by 14 to find the value of x:
\[ x = \frac{70}{14} \]
\[ x = 5 \]

**Hint:** To isolate the variable, perform the same operation on both sides of the equation.

### Step 5: Find the Breadth
Now that we have the value of x, we can find the breadth (B):
\[ B = 3x = 3(5) = 15 \text{ meters} \]

**Hint:** Substitute the value of x back into the expression for breadth.

### Conclusion
The breadth of the rectangular field is **15 meters**.