## OG 2020: Question No. 328

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

- JK = 10
- 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__

__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__

__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__

__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)__

__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.