Question

一个长方形的对角线长度为 $x$ ，并且长是宽的两倍。这个长方形的面积是多少？

A rectangle with a diagonal of length $x$ is twice as long as it is wide. What is the area of the rectangle?

$\dfrac{1}{4}x^2$

$\dfrac{2}{5}x^2$

$\dfrac{1}{2}x^2$

$x^2$

$\dfrac{3}{2}x^2$

答案：B

知识点：矩形勾股定理面积

难度评级：1100

解答：

设宽为 $w$ ，长为 $2w$ 。由勾股定理， $x^2 = w^2 + (2w)^2 = 5w^2$ ，所以 $w^2 = \dfrac{x^2}{5}$ 。长方形面积为 $w \cdot 2w = 2w^2 = \dfrac{2}{5}x^2$ 。

所以正确答案是 B。

Let the width be $w,$ so the length is $2w.$ Then $x^2 = w^2 + (2w)^2 = 5w^2,$ giving $w^2 = \dfrac{x^2}{5}.$ The area is $w \cdot 2w = 2w^2 = \dfrac{2}{5}x^2.$

Thus, the correct answer is B.

2005 AMC 10A 第 4 题

答案：B

难度评级：1100

解答：

其他年份的第 4 题