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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.