Since triangles XYZ and JKL are similar (denoted by the symbol "~"), the ratios of their corresponding sides are equal.
Given the measurements:
-
For triangle XYZ:
- Side XY = 8.7
- Side XZ = 8.2
- Side YZ = 7.8
-
For triangle JKL:
- Side JK = 12.18
- Side KL = ?
To find the length of KL, we can set up a ratio between the sides of the two triangles:
\[ \frac{XY}{JK} = \frac{YZ}{KL} \]
From the information given, we can use side XY and JK:
\[ \frac{8.7}{12.18} = \frac{7.8}{KL} \]
Now, we will cross-multiply to solve for KL:
\[ 8.7 \cdot KL = 7.8 \cdot 12.18 \]
Calculating the right side:
\[ 7.8 \cdot 12.18 = 95.376 \]
Now we have:
\[ 8.7 \cdot KL = 95.376 \]
Next, we divide both sides by 8.7 to isolate KL:
\[ KL = \frac{95.376}{8.7} \]
Calculating KL:
\[ KL \approx 10.95 \]
This value is closest to 10.92, so the measurement of KL is:
KL = 10.92