AMC 8 1985 Problem 12

AMC8 1985 年第 12 题

四边形与多边形★★★☆☆

A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are

6.2 \text cm

8.3 \text cm

and

9.5 \text cm

. The area of the square is

一个正方形和一个三角形周长相等。三角形三边长分别为

6.2 \text{ cm}

、

8.3 \text{ cm}

和

9.5 \text{ cm}

。正方形的面积是

正确答案 · Correct Answer

解析 · Solution

Solution 1

The perimeter of the triangle is

6.2+8.3+9.5=24\text{ cm}

. Therefore, the perimeter of the square is also

24 \text{ cm}

, so its side length is

\displaystyle \frac{24}{4}=6 \text{ cm}

and its area is

6^2= 36 \text{ cm}^2

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