AMC10 2010 A

AMC10 2010 A · Q2

AMC10 2010 A · Q2. It mainly tests Linear equations, Coordinate geometry.

Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?

四个相同的正方形和一个矩形拼在一起形成一个大正方形，如图所示。矩形的长是其宽的几倍？

(A) $\frac{5}{4}$ $\frac{5}{4}$

(B) $\frac{4}{3}$ $\frac{4}{3}$

(D) 2 2

(E) 3 3

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $s$ be the side length of the smaller square. Then the length of the rectangle is $4s$, and the width is $4s - s = 3s$. Hence the rectangle length is $\frac{4s}{3s} = \frac{4}{3}$ times as large as its width.

答案（B）：设 $s$ 为较小正方形的边长。那么长方形的长度为 $4s$，宽度为 $4s - s = 3s$。因此，长方形的长度是其宽度的 $\frac{4s}{3s} = \frac{4}{3}$ 倍。

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