AMC10 2009 B

AMC10 2009 B · Q4

AMC10 2009 B · Q4. It mainly tests Triangles (properties), Area & perimeter.

A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape. The parallel sides of the trapezoid have lengths 15 and 25 meters. What fraction of the yard is occupied by the flower beds?

一个矩形院子里有两个形状全等、直角等腰三角形的花坛。院子剩余部分呈梯形。梯形的平行边长分别为15米和25米。花坛占院子的几分之几？

(A) $\frac{1}{8}$ $\frac{1}{8}$

(B) $\frac{1}{6}$ $\frac{1}{6}$

(D) $\frac{1}{4}$ $\frac{1}{4}$

(E) $\frac{1}{3}$ $\frac{1}{3}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Each triangle has leg length $\frac{1}{2}\cdot(25-15)=5$ meters and area $\frac{1}{2}\cdot 5^2=\frac{25}{2}$ square meters. Thus the flower beds have a total area of 25 square meters. The entire yard has length 25 and width 5, so its area is 125. The fraction of the yard occupied by the flower beds is $\frac{25}{125}=\frac{1}{5}$.

答案（C）：每个三角形的直角边长为 $\frac{1}{2}\cdot(25-15)=5$ 米，面积为 $\frac{1}{2}\cdot 5^2=\frac{25}{2}$ 平方米。因此花坛的总面积为 25 平方米。整个院子的长为 25、宽为 5，所以面积为 125。花坛占院子的比例为 $\frac{25}{125}=\frac{1}{5}$。

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