Given that triangles \( \triangle JKL \sim \triangle PKQ \), we can use the property of similar triangles that states the ratios of corresponding sides are equal.
From the question, we know:
- \( KP = 14 , \text{m} \)
- \( JK = 56 , \text{m} \)
- \( KQ = 21 , \text{m} \)
Let \( KL = x \). Since the triangles are similar, we can set up the following proportion based on the sides:
\[ \frac{JK}{KP} = \frac{KL}{KQ} \]
Substituting the known lengths into the proportion gives:
\[ \frac{56}{14} = \frac{x}{21} \]
Now we simplify \( \frac{56}{14} \):
\[ \frac{56}{14} = 4 \]
So the equation becomes:
\[ 4 = \frac{x}{21} \]
To find \( x \), we can cross-multiply:
\[ 4 \cdot 21 = x \] \[ x = 84 , \text{m} \]
Thus, the length of \( KL \) is:
84 m
So the correct answer is:
84 m