Question

Triangle JKL is similar to Triangle PKQ and line KP=14m, line JK= 56 m, and line KQ=21 m. What is the length of line KL?

5.25 m
84 m
72 m
34 m

Answer 1

Since triangles JKL and PKQ are similar, the ratios of corresponding sides are equal. We can use the lengths of the sides provided to set up a proportion.

We know:
- \( KP = 14 \, \text{m} \)
- \( JK = 56 \, \text{m} \)
- \( KQ = 21 \, \text{m} \)

We need to find \( KL \).

The corresponding sides in the triangles are:
- Side \( KP \) corresponds to side \( JK \)
- Side \( KQ \) corresponds to side \( KL \)

We can set up the ratio as follows:

\[
\frac{JK}{KP} = \frac{KL}{KQ}
\]

Substituting the known values:

\[
\frac{56}{14} = \frac{KL}{21}
\]

Calculating the left side of the equation:

\[
\frac{56}{14} = 4
\]

Now we have:

\[
4 = \frac{KL}{21}
\]

To solve for \( KL \), we multiply both sides by \( 21 \):

\[
KL = 4 \times 21 = 84 \, \text{m}
\]

Thus, the length of line \( KL \) is \( \boxed{84 \, \text{m}} \).