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
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
We need to determine
- The area, in square meters, of the piece of land.
Approach & Working
As 52 + 122 = 132, 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.
