Question

一个长方形停车场的对角线长 $25$ 米，面积为 $168$ 平方米。该停车场的周长是多少米？

A rectangular parking lot has a diagonal of $25$ meters and an area of $168$ square meters. In meters, what is the perimeter of the parking lot?

$52$

$58$

$62$

$68$

$70$

答案：C

知识点：矩形勾股定理代数变形

难度评级：1370

解答：

设长方形边长为 $l,w$ 。要求的是 $2(l+w)$ 。由勾股定理，并且 $lw = 168$ 。 $25 = \sqrt{l^2+w^2}$ $l^2+w^2 = 625$

因此所以 $l+w = 31$ ，周长为 $31\cdot 2=62$ 。 $\begin{align*}l^2+2lw+ w^2 &= (l+w)^2 \\&= 961 \\&= 31^2.\end{align*}$

所以正确答案是 C。

Let the side lengths be $l,w.$ We wish to find $2(l+w).$ From the Pythagorean Theorem, we get $25 = \sqrt{l^2+w^2}$ $l^2+w^2 = 625$ We also know $lw = 168.$

As such $\begin{align*}l^2+2lw+ w^2 &= (l+w)^2 \\&= 961 \\&= 31^2.\end{align*}$ This makes $l+w = 31,$ and as such, our answer is $31\cdot 2=62.$

Thus, the correct answer is C .

2011 AMC 10B 第 14 题

答案：C

难度评级：1370

解答：

其他年份的第 14 题