## OGQR 2020: Question No. 210

What is the perimeter of triangle ABC?

- AB = 16 inches
- ΔABC is equilateral.

Source | OGQR 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Triangle |

Difficulty | Easy |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

We are given:

- A triangle ABC.

We need to find its perimeter.

- So, we need the length of all the sides of the triangle.

As we do not have any more relevant information, let us now analyse the statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

*“AB = 16 inches”*

From this information, we cannot find the answer to the question as we are not given the lengths of other two sides.

Thus, statement 1 is not sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

*“ΔABC is equilateral.”*

For an equilateral triangle, the perimeter of the triangle = 3 × Side.

- However, we do not know the length of the side of the triangle.
- Thus, statement 2 is not sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

From Statement 1:

- AB = 16 inches

From Statement 2:

- Area of the triangle = 3 × Side.

By using both the statements, we can find the perimeter of the triangle.

Hence, we can find the answer by combining both the statements together.

- Thus, the correct answer choice is option C.

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