Question

在这个 $100$ 英寸乘 $100$ 英寸的正方形中，四个全等 L 形区域中每一个的面积都是总面积的 $\dfrac{3}{16}$ 。中心正方形的边长是多少英寸？

The area of each of the four congruent L-shaped regions of this $100$ -inch by $100$ -inch square is $\dfrac{3}{16}$ of the total area. How many inches long is the side of the center square?

$25$

$44$

$50$

$62$

$75$

答案：C

知识点：正方形（几何）面积

难度评级：980

解答：

四个 L 形区域合计占 $4 \times \dfrac{3}{16} = \dfrac34$ 的大正方形，所以中心正方形占剩下的 $\dfrac14$ 。

大正方形面积为 $100 \times 100 = 10000$ 平方英寸，所以中心正方形面积为 $\dfrac14 \times 10000 = 2500$ ，边长为 $\sqrt{2500} = 50$ 英寸。

所以正确答案是 C。

The four L-shaped regions cover $4 \times \dfrac{3}{16} = \dfrac34$ of the square, so the center square is the remaining $\dfrac14$ of the total area.

The total area is $100 \times 100 = 10000$ square inches, so the center square has area $\dfrac14 \times 10000 = 2500,$ and its side is $\sqrt{2500} = 50$ inches.

Thus, the correct answer is C .

1995 AMC 8 第 18 题

答案：C

难度评级：980

解答：

其他年份的第 18 题