What is the best way to explain such type of questions to 11 years old? and also please let me know the answer as well. Thank you.
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In this case you can talk about triangles that point up and those that point down, along with the two (only two) different sizes. Specifically here there are are only three directions of lines, so every triangle needs one of each type of line. – Joffan Jun 19 '18 at 20:29
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I would say that, besides the obvious small triangles, it is also possible for these small triangles to come together and create larger triangles. Then simply point out a place or two where this happens. – Shaun_the_Post Jun 19 '18 at 20:30
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Color with yellow the little ones (counting them). Then color with blue the big ones (counting them). – Mauro ALLEGRANZA Jun 19 '18 at 20:30
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The idea is that all triangles must have same sidelengths, so it boils down to counting all with side length $1$, then $2$. – I was suspended for talking Jun 19 '18 at 20:30
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There is a natural assumption that the sides of the triangles have to be made up of the solid line segments in the diagram.
You need to find a systematic way of counting.
First note that every triangle you will be counting has three sixty degree angles and will therefore be equilateral.
Second, note that all such equilateral triangles will have precisely one side which is horizontal.
Third, each horizontal line can be part of at most two triangles - one above it and one below it.
So first look at horizontal segments of length $1$. The two at the top and the one at the bottom are part of just one triangle of side $1$ and the others count for two.
Then look at the horizontal line segments of length $2$ in a similar way. And then longer sides until you are done.
(note the side $1$ triangles are easy to count anyway, but it is sometimes useful to have a single systematic approach, rather than different approaches for different sizes - also you have an easy check on your count)
Mark Bennet
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