1954 AMC 12 第 29 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
29.
若一个直角三角形的两条直角边之比为 ，则从直角顶点向斜边作垂线后，斜边上对应两段之比为：
If the ratio of the legs of a right triangle is then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex is:
小提示：
斜边上的两段分别是两条直角边在斜边上的投影
The two hypotenuse segments are the projections of the legs
大提示：
由相似关系，它们的比等于对应直角边平方之比
By similarity, their ratio is the ratio of the squares of the corresponding legs
解答：
若两条直角边长为 和 ，则它们在斜边上的投影长为 和 。因此两段之比为 。当 时，该比为 。
因此，正确答案是 A。
If the legs have lengths and their projections on the hypotenuse have lengths and Their ratio is therefore With this is
Thus, the correct answer is A.
其他年份的第 29 题
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- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1955 AMC 12
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