Question

一个长方形院子里有两个花坛，形状是全等的等腰直角三角形。院子的其余部分是如图所示的梯形。梯形的两条平行边长度分别为 $15$ 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?

$\dfrac{1}{8}$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

答案：C

知识点：面积比三角形面积梯形

难度评级：1100

解答：

两条平行边相差 $25 - 15 = 10$ ，所以每个三角形的直角边为 $\dfrac{10}{2} = 5$ ，面积为 $\dfrac{1}{2} \cdot 5^2 = \dfrac{25}{2}$ 。两个花坛总面积为 $25$ 。

长方形尺寸为 $25$ 乘 $5$ ，面积为 $125$ ，花坛所占比例为 $\dfrac{25}{125} = \dfrac{1}{5}$ 。

所以正确答案是 C。

The parallel sides differ by $25 - 15 = 10,$ so each triangle has legs $\dfrac{10}{2} = 5$ and area $\dfrac{1}{2} \cdot 5^2 = \dfrac{25}{2}.$ The two beds total $25.$

The rectangle measures $25$ by $5,$ so its area is $125,$ and the fraction occupied is $\dfrac{25}{125} = \dfrac{1}{5}.$

Thus, the correct answer is C.

2009 AMC 12B 第 4 题

答案：C

难度评级：1100

解答：

其他年份的第 4 题