AMC 8 1995 Problem 18

AMC8 1995 年第 18 题

面积与周长（综合）★★★☆☆

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?

在这个 100 英寸 × 100 英寸的正方形中，四个全等 L 形区域各占总面积的 3/16。中心正方形的边长是多少英寸？

A.25
B.44
C.50
D.62
E.75

正确答案 · Correct Answer

解析 · Solution

Solution 1

The area taken up by the L's is

\displaystyle 4 * \frac{3}{16} = \frac{3}{4}

of the area of the whole square. What remains has

\displaystyle \frac{1}{4}

of the area of the larger square.

\displaystyle \frac{100*100}{4} = \frac{100}{2} * \frac{100}{2} = 50*50

is the area of the smaller square, so its side length is 50.

\text{(C)}

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