Given that the triangles \( \triangle JKL \sim \triangle PKQ \), we can use the properties of similar triangles to find the length of \( LQ \).
From the information provided, we know the following corresponding lengths from the similar triangles:
- \( JL = 15 \) inches (from \( \triangle JKL \))
- \( KQ = 17 \) inches (from \( \triangle PKQ \))
- \( PK = 15 \) inches (from \( \triangle PKQ \))
Let's denote the length of \( LQ \) as \( x \).
Since the triangles are similar, the ratios of the corresponding sides are equal. Thus, we can set up the following proportion based on the sides we have:
\[ \frac{JL}{PK} = \frac{LQ}{KQ} \]
Substituting the known values into the proportion:
\[ \frac{15}{15} = \frac{x}{17} \]
Simplifying the left side:
\[ 1 = \frac{x}{17} \]
Now, to find \( x \):
\[ x = 17 \]
Thus, the length of \( LQ \) is:
\[ \boxed{17} \text{ inches} \]
1 answer