AMC 8 1985 Problem 19
AMC8 1985 年第 19 题
面积与周长（综合）★★★☆☆
If the length and width of a rectangle are each increased by 10%, then the perimeter of the rectangle is increased by
如果矩形的长和宽各增加 10%，则矩形的周长增加了
- A.1%
- B.10%
- C.20%
- D.21%
- E.40%
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
Let , , and be the original width, length, and perimeter of the rectangle, respectively. Then p = 2(w+l).
The width and length are increased to 1.1w and 1.1l, respectively. Therefore, the new perimeter is , or 10% more than the original perimeter.
Since each side is scaled by a factor of 1.1, the new rectangle is similar to the original, and therefore its perimeter is also scaled by a factor of 1.1, that is, a 10% increase.
Suppose the original rectangle is a square of side length 10, so its perimeter is . After scaling, its sides will have length , so its perimeter will be . Therefore, the new perimeter is times the original perimeter, a 10% increase.
继续练习