1985 AMC 8 第 12 题

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12.

一个正方形和一个三角形的周长相等。三角形三边长分别为 6.26.2 厘米、8.38.3 厘米和 9.59.5 厘米。这个正方形的面积是多少平方厘米?

A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.26.2 cm, 8.38.3 cm, and 9.59.5 cm. The area of the square, in square centimeters, is

24 cm224 \text{ cm}^2

36 cm236 \text{ cm}^2

48 cm248 \text{ cm}^2

64 cm264 \text{ cm}^2

144 cm2144 \text{ cm}^2

答案:B
知识点:周长正方形(几何)
难度评级:730
解答:

三角形周长是 6.2+8.3+9.5=246.2 + 8.3 + 9.5 = 24 厘米,所以正方形周长也是 2424 厘米。

正方形边长是 244=6\dfrac{24}{4} = 6 厘米,因此面积是 62=36 cm26^2 = 36 \text{ cm}^2

所以正确答案是 B

The triangle's perimeter is 6.2+8.3+9.5=246.2 + 8.3 + 9.5 = 24 cm, so the square also has perimeter 2424 cm.

The square's side is 244=6\dfrac{24}{4} = 6 cm, so its area is 62=36 cm2.6^2 = 36 \text{ cm}^2.

Thus, the correct answer is B .

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