In ΔJKL, what is the length of segment JL

In ΔJKL, what is the length of segment JL?

  1. JK = 10
  2. KL = 5

Answer

As angle KJL = 30°, angle JKL = 60°, angle JLK = 180° - (30° + 60°) = 90°

Hence, ΔJKL is a 30°-60°-90° triangle, and its sides are in the ratio 1 : √3 : 2.

KL: JL: JK = 1 : √3 : 2

Therefore, to find the length of any side, you need to know the length of any of the other two sides.

Statement 1: JK = 10.

Using the side ratio, we can determine the value of JL, with the help of the value of JK. Hence, statement 1 is sufficient to answer the question.

Statement 2: KL = 5.

Using the side ratio, we can determine the value of JL, with the help of the value of KL. Hence, statement 2 is sufficient to answer the question.

The correct option is D.