AMC 8 2026 Problem 3
AMC8 2026 年第 3 题
三角形★★☆☆☆
Haruki has 24 centimeters of wire. He cuts the wire and bends it into the following shapes, one at a time:
- A regular hexagon with side length 5 cm
- A square of area 36 cm²
- A right triangle whose legs are 6 and 8 cm long
Which of the shapes can Haruki make?
Haruki 有 24 厘米长的铁丝。他剪断铁丝并把它弯成以下形状，一次做一个：
- 边长为 5 cm 的正六边形 - 面积为 36 cm² 的正方形 - 两条直角边分别为 6 cm 和 8 cm 的直角三角形
Haruki 能做出哪些形状？
- A.Triangle only / 仅三角形
- B.Hexagon and square only / 仅正六边形和正方形
- C.Hexagon and triangle only / 仅正六边形和三角形
- D.Square and triangle only / 仅正方形和三角形
- E.Hexagon, triangle, and square / 正六边形、三角形和正方形
正确答案 · Correct Answer
D
解析 · Solution
解法1
逐一计算各图形周长并与 24 cm 比较。正六边形（边长 5）：6×5=30 cm > 24，不可行。正方形（面积 36，边长 6）：4×6=24 cm，可行。直角三角形（直角边 6 和 8，斜边 10）：6+8+10=24 cm，可行。只有正方形和直角三角形满足条件。
利用选项快速排除。正六边形周长 30 cm 已超 24，直接排除所有含正六边形的选项。正方形周长 24 cm 可行，剩余选项中仅一个包含正方形，无需计算三角形即可锁定答案。根本区别：此方法依赖选项排除，不需求出所有图形的周长。
Solution 1
Find the perimeter of each shape and compare to 24 cm. Regular hexagon (side 5): 6×5 = 30 cm > 24. Square (area 36, side 6): 4×6 = 24 cm. Right triangle (legs 6 and 8, hypotenuse 10): 6+8+10 = 24 cm. Only the square and right triangle have perimeter ≤ 24 cm.
Use the answer choices to save time. The hexagon alone has perimeter 30 cm > 24, so any answer that includes the hexagon is wrong. Eliminate those. The square has perimeter 24 cm, which works. Only one remaining choice includes the square — no need to compute the triangle at all. Answer: square and triangle.
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