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## 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. Payal Tandon
Co-founder, e-GMAT
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