Question

Please Help (includes picture):
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The figure below represents a figure with a total of 120 triangles and n points labeled as vertices on the horizontal base. What is the value of n?

Answer 1

Since two A's form a triangle, and there are 120 triangles, what does that say about A(n) ?

Answer 2

In other words, look at A(1) - A(5), how many triangles were made?

Answer 3

5 triangles consisting of just 1 triangle, 5 more triangles consisting of two triangles (each), two triangles consisting of 3 triangles (each), and 1 triangle consisting of four triangles

Answer 4

i see 4 triangles consisting of just 1 triangle, 2 consisting of points A(1) - A(3) and A(1) - A(3), 1 consisting of A(1) - A(4), 1 consisting of A(2) - A(5), and 1 consisting of A(1) - A(5)

So a total of 9 different triangles for A(1) - A(5)

would you agree?

Answer 5

Yes, I accidentally included an extra triangle in my counting, my mistake.

Answer 6

so for 5 different points, we have 9 triangles.
A(1)-A(5) = 9
A(5) - A(9) = 18
A(9) - A(13) = 27
13 - 17 = 36
17 - 21 = 45
21 - 25 = 54
25 - 29 = 63
29 - 33 = 72
33 - 37 = 81
37 - 41 = 90
41 - 45 = 99
45 - 49 = 108
49 - 53 = 117

We need 3 more triangles, so how many more A's do we need to add?

Answer 7

Would it be 1?
I'm leaning a little bit more towards one, but I think it might also be two, I'm not quite sure.

Answer 8

we are guaranteed to have 117 triangles at 53, so we if add A(54) we get 118, if we add A(55) we get 119, and we get another triangle from 54 and 55, so we have 120 triangles