Question

一个长方形院子里有两块花坛，形状为全等的等腰直角三角形。院子的其余部分如图所示为梯形。梯形的平行边长为 $15$ 米和 $25$ 米。花坛占整个院子的几分之几？

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

$\dfrac18$

$\dfrac16$

$\dfrac15$

$\dfrac14$

$\dfrac13$

答案：C

知识点：三角形面积梯形面积比

难度评级：960

解答：

两条平行边相差 $25-15=10$ ，平均分到两个三角形上，所以每个等腰直角三角形的直角边为 $5$ ，面积为 $\dfrac12\cdot5^2=\dfrac{25}{2}$ 。

两块花坛总面积为 $25$ 平方米。长方形长 $25$ 、宽 $5$ ，面积为 $125$ 。所占比例为 $\dfrac{25}{125}=\dfrac15$ 。

所以正确答案是 C。

The two parallel sides differ by $25-15=10,$ split evenly between the two triangles, so each isosceles right triangle has legs of length $5$ and area $\dfrac12\cdot5^2=\dfrac{25}{2}.$

Together the beds cover $25$ square meters. The rectangle has length $25$ and width $5,$ so area $125.$ The fraction is $\dfrac{25}{125}=\dfrac15.$

Thus, the correct answer is C.

2009 AMC 10B 第 4 题

答案：C

难度评级：960

解答：

其他年份的第 4 题