## OGQR 2020: Question No. 90

On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimetres. If 1 centimetre on the drawing represents 3 meters, what is the area, in square meters, of the piece of land?

Source | OGQR 2020 |

Type | Problem Solving |

Topic | Geometry |

Sub-Topic | Triangle / Unit Conversion |

Difficulty | Medium |

### Solution

__Given__

__Given__

In this question, we are given

- On a scale drawing of a triangular piece of land, the sides of the triangle have lengths 5, 12, and 13 centimetres.
- 1 centimetre on the drawing represents 3 meters.

__To Find__

__To Find__

We need to determine

- The area, in square meters, of the piece of land.

__Approach & Working__

__Approach & Working__

As 5^{2} + 12^{2} = 13^{2}, we can say the land is in the shape of a right-angled triangle.

- Side length 5, converted into meters = 5 * 3 = 15 meters
- Side length 12, converted into meters = 12 * 3 = 36 meters
- Therefore, the area of the piece of land = 1/2 * 15 * 36 sq. m. = 270 sq. m.

Hence, the correct answer is option D.