Tickbox Quiz #11 Q 7 and 10

[hiiie28]

Q7.

I’m stuck on why AC is 1/4 of AE. Greg gives example by saying that if AE was 4n then AC would be n. Why is that?

Q10.

Greg says that if the smallest triangle’s area is 1 then the next bigger triangle’s area would be 4 and then largest is 9. Why is that?

I think I lack in this triangle subject. Help on the questions and also recommendations on what prepswift videos I should watch would be very much appreciated. @Leaderboard @ganesh

[cylverixxx]

Maybe it helps to review similar triangles

[ganesh]

@hiiie28

Greg says that if the smallest triangle’s area is 1 then the next bigger triangle’s area would be 4 and then largest is 9. Why is that?

Let’s say there is triangle A, and triangle B (similar to A, but all the sides are multiplied by 2 → the scale is 2)

If the base and height of A are x and y respectively, then::

1. The area of A is \frac{1}{2} \times x \times y
2. The area of B is \frac{1}{2} \times 2x \times 2y

Since the area of 2D shapes depend on 2 dimensions (base and height) the scale is applied twice, so the area increases by scale^2