Given that triangles JKL and PKQ are similar (noted as \( JKL \sim PKQ \)), we can use the properties of similar triangles to find the length of \( KL \).
From the similarity of the triangles, we can set up a ratio using the lengths of the corresponding sides:
\[ \frac{JK}{PK} = \frac{KL}{KQ} \]
We know:
- \( JK = 56 , m \)
- \( KQ = 21 , m \)
- \( KP = 14 , m \)
Let \( KL = x \). Thus, we have:
\[ \frac{56}{14} = \frac{x}{21} \]
Now, simplify the left side:
\[ \frac{56}{14} = 4 \]
So the equation now is:
\[ 4 = \frac{x}{21} \]
To solve for \( x \), multiply both sides by 21:
\[ x = 4 \times 21 = 84 , m \]
Thus, the length of \( KL \) is \( \boxed{84 , m} \).