2018Q9(b)(iii)Similarity (With Applications to Maps and Models)

NumericalEasy1 mark

9(b)

In ΔPQR, MN is parallel to QR and PM / MQ = 2 / 3

Figure for this question

Find, Area of ΔOMN : Area of ΔORQ

Topic: Similarity / scale factor

Previous-year question practice database

Answer

Exam answer

From part (i):

MN/QR = 2/5

The corresponding triangles are similar.

Therefore the ratio of their areas is the square of the corresponding-side ratio:

Area of ΔOMN : Area of ΔORQ = (2/5)²

= 4/25

Answer:

4 : 25.

Explanation

For similar triangles, areas are proportional to the squares of corresponding sides. The linear ratio is 2:5, so the area ratio is 4:25.

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