1998 AMC 12 第 10 题

Question

如图所示，一个大正方形被分成一个小正方形和围绕它的四个全等长方形。每个全等长方形的周长为

14

。大正方形的面积是多少？

A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimeter of each of the congruent rectangles is

14.

What is the area of the large square?

49

64

100

121

196

设一个长方形的两条边长为

x

和

y

Let the sides of one rectangle be

x

and

y

大正方形的边长为

x+y

The side length of the large square is

x+y

若长方形的边长为

x,y

，则

2x+2y=14

，所以

x+y=7

。大正方形的边长为

x+y

，故其面积为

7^2=49

。正确答案是 A。

If a rectangle has sides

x,y,

then

2x+2y=14,

so

x+y=7.

The large square has side

x+y,

hence area

7^2=49.

The correct answer is A.

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