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In ΔJKL shown above, what is the length of segment JL? – OG 2020 Question #328 with Solution

A 2 min read

OG 2020: Question No. 328

In ΔJKL shown above, what is the length of segment JL?

  1. JK = 10
  2. KL = 5
Source OG 2020
Type Data Sufficiency
Topic Geometry
Sub-Topic Triangles
Difficulty Easy – Medium

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

  • The diagram of a triangle ΔJKL, where angle KJL = 30° and angle JKL = 60°

We need to determine

  • The length of the segment JL

As angle KJL = 30° and angle JKL = 60°, we can say angle JLK = 180° – (30° + 60°) = 90°

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

  • Or in other words, KL: JL: JK = 1: √3: 2.
  • Therefore, to find the length of any side, we need to know the length of any of the other two sides.

With this understanding, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

As per the information given in 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.

 

Step 4: Analyse Statement 2

As per the information given in 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.

 

Step 5: Combine Both Statements Together (If Needed)

Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

 

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