Question

There is a triangle labeled JKL, and around the middle of the triangle there is a line segment going through it horizontally labeled PQ.

Triangle JKL - triangle PKQ, and line KP = 14m, line JK = 56 m, and line KQ = 21 m. What is the length of line KL?
A. 34 m
B. 84 m
C. 5.25 m
D. 72 m

Answer 1

To find the length of line segment KL in triangle JKL, we can use the property of similar triangles. Since line segment PQ is horizontal and goes through triangle JKL, it creates triangle PKQ, which is similar to triangle JKL.

For similar triangles, the ratios of corresponding sides are equal. From the problem, we have:

1. Segment KP corresponds to segment JK.
2. Segment KQ corresponds to segment KL.

Let's denote the length of line KL as \( x \).

The corresponding sides give us the following ratio:

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

Substituting in the values we know:

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

Now, simplify the left side:

\[
\frac{14}{56} = \frac{1}{4}
\]

This yields:

\[
\frac{1}{4} = \frac{21}{x}
\]

Cross-multiplying gives:

\[
1 \cdot x = 4 \cdot 21
\]

\[
x = 84
\]

Thus, the length of line KL is \(84 \, m\).

The correct answer is B. 84 m.