2019 AMC 8 第 2 题

先试着解答 2019 AMC 8 第 2 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2019 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

2.

三个全等的矩形拼成了矩形 ABCDABCD,如下图所示。已知每个小矩形较短边长为 55 英尺,矩形 ABCDABCD 的面积是多少平方英尺?
Three identical rectangles are put together to form rectangle ABCD,ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 55 feet, what is the area in square feet of rectangle ABCD?ABCD?
4545
7575
100100
125125
150150
答案:E
知识点:矩形面积
小提示:
每个小矩形的长边等于两个短边
The long side of each small rectangle is two short sides
大提示:
大矩形是 1010 英尺乘 1515 英尺
The big rectangle is 1010 feet by 1515 feet
视频讲解:
解答视频缩略图
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文字解答:
从图中可见,小矩形的长边等于两个短边,所以长边为 2⋅5=102 \cdot 5 = 10 英尺。
大矩形的一边为 BC=10BC = 10 英尺,另一边为 DC=10+5=15DC = 10 + 5 = 15 英尺。面积为 10⋅15=15010 \cdot 15 = 150 平方英尺。
正确答案是 E。
From the figure, we can see that the longer side has the same length as two of the shorter sides. This makes it 2⋅5=102 \cdot 5 = 10 feet long.
This tells us that BC=10BC = 10 feet and DC=10+5=15DC = 10 + 5 = 15 feet. Therefore, the area is 10⋅15=15010 \cdot 15 = 150 square feet.
Thus, the correct answer is E.
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