Triangle Wossname

How many triangles are there in the figure above?

8 12 16 20

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Chung Kevin
Apr 15, 2016

Let us find all the smallest triangles first. The diagram directly below us tells us that there are 8 smallest triangle.

By repeating this process, we can see that there are 8 larger triangles as shown below.

Once again, we can see that there are 4 larger triangles as shown below.

This gives us a total of 8 + 8 + 4 = 20 8+8+4 =\boxed{20} triangles.

And this can be thought of in terms of a generating rule by observing that if the biggest big square doesn't have the square inscribed in it there will be no triangles in the figure and therefore that that inscribed square generates all the possible triangles which generation can be seen by taking as an unity the smallest squares of the biggest square (observing the number of triangles generated for 1 small square , then for 2 and so on) but this would give at first sight an answer of just 16 triangles generated by this rule. So , then comes the problem of how it can be done for some situation where the number of unit squares is not an integer therefore making in this terms an interpretation of in some way "imperfect" value for the generation of this rule which implies that if for a number of squares there is a "continuity" (of the surface of a triangle , in other words the possible extension of an triangle on more than 2 unit squares would be imperfect since it implies more than just 1 line of the triangle) after the continuity of only one line which intersects those squares (which is what is implicitly thought of by the generation rule) under the monotony of other continuous line drawn from the same point but this (synthetic) approach already sounds not clear enough though pretty interesting anyways.

A A - 5 years, 1 month ago
Chew-Seong Cheong
Jul 31, 2017

Every side of the big square gives 5 triangles, therefore, 4 sides give 5 × 4 = 20 5 \times 4 = \boxed{20} .

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...