AMC 8 2018 Problem 9
AMC8 2018 年第 9 题
四边形与多边形★★☆☆☆
Tyler is tiling the floor of his 12-foot by 16-foot living room. He plans to place one-foot by one-foot square tiles to form a border along the edges of the room and to fill in the rest of the floor with two-foot by two-foot square tiles. How many tiles will he use?
正在将他起居室 12 英尺ｘ16 英尺的地面用瓷砖贴起来。他打算用 1 英尺ｘ1 英尺的方形瓷砖沿着地板的边缘贴起来，地板的其他部分用 2 英尺ｘ2 英尺的方形瓷砖填满。问他最终总共使用了多少块瓷砖？
- A.48
- B.87
- C.91
- D.96
- E.120
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
He will place tiles around the border. For the inner part of the room, we have square feet. Each tile takes up , or 4 square feet, so he will use tiles for the inner part of the room. Thus, the answer is 52+35= 87
The area around the border: . The area of tiles around the border: . Therefore, is the number of tiles around the border. The inner part will have (12 - 2)(16 - 2) = 140. The area of those tiles are . is the amount of tiles for the inner part. So, 52 + 35 = 87.
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