2014 maths 2U paper

[sodiumziha]

This is probably dead easy, but the sample answer for Question 15 (b) (iii), says that "Ratio of areas of similar triangles is equal to the square of the ratio of the sides". I never got taught that, is that common knowledge or what? Idk, these kinds of questions with abstract reasoning or whatever always get me. Any tips?

[fan96]

I remember learning this in Year 10, though not in the HSC course.

But if you start from the observation that the perpendicular heights of the two similar triangles are in the same ratio as the sides then you could finish the question from there by using the area formula.