If `(a)/(7) = (b)/(9) = (e)/(11)`, then find a : b: c

Options

A. `11:9 :7`
B. `9 :7: 11`
C. `7 :9:11`
D. `11 :7:9`

Answer

To solve the problem, we start with the given ratios:

\[ \frac{a}{7} = \frac{b}{9} = \frac{c}{11} \]

Let's denote the common ratio as \( k \). This means we can express \( a \), \( b \), and \( c \) in terms of \( k \):

1. From \(\frac{a}{7} = k\), we can express \( a \) as:
\[ a = 7k \]

2. From \(\frac{b}{9} = k\), we can express \( b \) as:
\[ b = 9k \]

3. From \(\frac{c}{11} = k\), we can express \( c \) as:
\[ c = 11k \]

Now, we have \( a \), \( b \), and \( c \) in terms of \( k \):
- \( a = 7k \)
- \( b = 9k \)
- \( c = 11k \)

Next, we need to find the ratio \( a : b : c \):
\[ a : b : c = 7k : 9k : 11k \]

Since \( k \) is common in all terms, we can simplify the ratio by canceling \( k \):
\[ a : b : c = 7 : 9 : 11 \]

Thus, the final answer is:
\[ \boxed{7 : 9 : 11} \]