AMC10 2008 A

AMC10 2008 A · Q2

AMC10 2008 A · Q2. It mainly tests Area & perimeter.

A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is 2:1. The ratio of the rectangle’s length to its width is 2:1. What percent of the rectangle’s area is inside the square?

在一个矩形内画一个正方形。矩形宽度与正方形边长的比为2:1。矩形长与宽的比为2:1。正方形占矩形面积的百分之多少？

(A) 12.5 12.5

(B) 25 25

(D) 75 75

(E) 87.5 87.5

Answer

Correct choice: (A)

正确答案：（A）

Solution

Let $x$ be the side length of the square. Then the area of the square is $x^2$. The rectangle has sides of length $2x$ and $4x$, and hence area $8x^2$. The fraction of the rectangle's area inside the square is $\frac{x^2}{8x^2} = \frac{1}{8}$ or 12.5%.

设正方形边长为$x$，则正方形面积为$x^2$。矩形边长为$2x$和$4x$，面积为$8x^2$。正方形占矩形面积的比例为$\frac{x^2}{8x^2} = \frac{1}{8}$，即12.5%。

Topics

GE.007 Area & perimeter