△JKL∼△PKQ\triangle JKL\sim\triangle PKQ, and KP¯¯¯¯¯¯¯¯=14\overline{KP}=14 m, JK¯¯¯¯¯¯¯¯=56\overline{JK}=56 m, and KQ¯¯¯¯¯¯¯¯=21\overline{KQ}=21 m. What is the length of KL¯¯¯¯¯¯¯¯\overline{KL}?

Answer 1

Since we have a similarity relationship between triangles JKL and PKQ, we know that the corresponding sides are proportional.

In particular, we have the following ratios:

JK / PK = KL / KQ

Substituting the given values, we get:

56 / 14 = KL / 21

Cross-multiplying, we have:

56 * 21 = 14 * KL

Simplifying:

1176 = 14 * KL

Dividing both sides by 14, we find:

KL = 1176 / 14 = 84

Therefore, the length of KL is 84 meters.