AMC 8 2014 Problem 6
AMC8 2014 年第 6 题
表达式与运算★☆☆☆☆
Six rectangles each with a common base width of 2 have lengths of 1, 4, 9, 16, 25 , and 36 . What is the sum of the areas of the six rectangles?
6 个矩形共同的宽是 2，它们的长分别是 1,4,9,16,25 和 36．那么这 6 个矩形的面积之和是多少？
- A.91
- B.93
- C.162
- D.182
- E.202
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
The sum of the areas is equal to . This is equal to 2(1+4+9+16+25+36), which is equal to . This is equal to our final answer of.
we can just multiply the common width 2 by each of the lengths 1 by 1, the sum would be 182. This is slow and grouping the lengths is easier to. The answer is still.
The formula for a consecutive perfect squared sum is , where is the number of terms from 1. Multiplying by the constant length 2 for area gives . Plugging in n = 6 gives.
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