AMC8 1995

AMC8 1995 · Q18

AMC8 1995 · Q18. It mainly tests Fractions, Area & perimeter.

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

这个100英寸×100英寸正方形中有四个全等的L形区域，每个区域的面积是总面积的3/16。中心正方形的边长有多少英寸？

(A) 25 25

(B) 44 44

(D) 62 62

(E) 75 75

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The four L-shaped regions account for $4\times\frac{3}{16}=\frac{12}{16}=\frac{3}{4}$ of the total area. That leaves $\frac{1}{4}$ of the total area for the center square, which yields $\left(\frac{1}{4}\right)(100\times100)=2500$ square inches. Thus the length of the side of the center square is $\sqrt{2500}=50$ inches.

答案（C）：四个 L 形区域占总面积的 $4\times\frac{3}{16}=\frac{12}{16}=\frac{3}{4}$。因此中心正方形占总面积的 $\frac{1}{4}$，其面积为 $\left(\frac{1}{4}\right)(100\times100)=2500$ 平方英寸。于是中心正方形的边长为 $\sqrt{2500}=50$ 英寸。

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