The ratio between the length and breadth of a rectangular board is 7:5. If the breadth of the board is 20.5cm, find the length in cm.

Options

A. 19.9
B. 24.3
C. 28.7
D. 14.6

Answer

To solve the problem, we need to find the length of the rectangular board given the ratio of length to breadth and the value of the breadth.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of length (L) to breadth (B) is given as 7:5. This can be expressed as:
\[ \frac{L}{B} = \frac{7}{5} \]

2. **Identify the Given Value**:
We are given the breadth (B) of the board as 20.5 cm.

3. **Set Up the Equation**:
Using the ratio, we can express the length in terms of the breadth:
\[ L = \frac{7}{5} \times B \]

4. **Substitute the Value of Breadth**:
Now, substitute the value of breadth (B = 20.5 cm) into the equation:
\[ L = \frac{7}{5} \times 20.5 \]

5. **Calculate the Length**:
First, calculate \( \frac{7}{5} \):
\[ \frac{7}{5} = 1.4 \]
Now, multiply this by 20.5:
\[ L = 1.4 \times 20.5 = 28.7 \text{ cm} \]

6. **Final Answer**:
Therefore, the length of the rectangular board is:
\[ L = 28.7 \text{ cm} \]