Update README.md

README.md

@@ -100,6 +100,47 @@ LLMは急速に進
 
 </details>
 
+<details><summary>A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the triangles is 21 inches, what is the perimeter, in inches, of the regular hexagon?</summary>
+  
+```
+To solve this problem, we need to determine the perimeter of a regular hexagon given that each of its equilateral triangles has a perimeter of 21 inches.
+
+First, let's recall some properties of regular polygons and their divisions into triangles.
+
+A regular hexagon consists of six sides and six vertices. When it is divided into six equilateral triangles, these triangles have equal side lengths. Each triangle must therefore be an equilateral triangle with all sides equal.
+
+Given that the perimeter of one of these triangles is 21 inches, we can use this information to find the length of each triangle's side. Since it's an equilateral triangle, all three sides are equal. Therefore, if the perimeter (sum of all sides) is 21 inches, then each side would be 21 / 3 = 7 inches long.
+
+Now, since the original figure is a regular hexagon made up of six such triangles, the entire perimeter should consist of the sum of all six triangle sides. So, multiplying the length of one side by the number of sides gives us the total perimeter.
+
+Let's compute that:
+
+Total perimeter of the hexagon = Number of triangles * Length per triangle
+= 6 * 7
+= 42
+
+Therefore, the perimeter of the regular hexagon is 42 inches.
+
+But wait, let me verify if there's another way to approach this problem to ensure I haven't missed anything.
+
+Another method could involve using the fact that in a regular hexagon, each internal angle is 120 degrees. However, perhaps more straightforwardly, since dividing a regular hexagon into six equilateral triangles splits each side into two segments: one from the central vertex to the midpoint of a side, which is part of the hexagon's side length, and the other segment is along the edge of the triangle, which is also part of the hexagon's perimeter but counted twice when adding up the triangles' perimeters. Wait, actually, no. Let me think again.
+
+Wait, when you divide the hexagon into six equilateral triangles, each triangle shares a side with adjacent triangles. The perimeter of each individual triangle is 21 inches, so the combined perimeter of all six triangles would be 6 times 21, which is indeed 126 inches. But that doesn't make sense because the hexagon itself is formed by the union of those six triangles. However, if we consider the perimeter as the outer boundary of the hexagon, then the perimeter of the hexagon would be the same as the perimeter of any single triangle plus the inner edges where they meet at the center. Hmm, maybe not directly applicable here.
+
+Alternatively, perhaps considering the area or something else, but since the question only asks for the perimeter, focusing on the division into triangles might be sufficient.
+
+So going back to the initial calculation: each triangle is 7 inches, multiplied by 6 gives 42. That seems correct.
+
+But just to double-check, let's visualize a regular hexagon. Each side of the hexagon is split into two parts by the centroid (the intersection point of the diagonals). In each triangle, the base is a side of the hexagon, and the height is half the distance between opposite sides. However, perhaps instead of getting bogged down in geometry, the key insight is recognizing that the perimeter of the hexagon is simply the sum of all the triangle sides, which we already calculated as 42 inches.
+
+Yes, that makes sense. The answer is 42 inches.
+
+**Final Answer**
+The perimeter of the regular hexagon is \boxed{42} inches.
+```
+
+</details>
+
 
 
 ### Sample Usage