HMMT 二月 2013 · 几何 · 第 1 题
HMMT February 2013 — Geometry — Problem 1
题目详情
英文原题
Jarris the triangle is playing in the ( x, y) plane. Let his maximum ycoordinate be k. Given that he has side lengths 6, 8, and 10 and that no part of him is below the x-axis, find the minimum possible value of k.
解析
英文解析
- Jarris the triangle is playing in the ( x, y ) plane. Let his maximum y coordinate be k . Given that hehas side lengths 6, 8, and 10 and that no part of him is below the x -axis, find the minimum possiblevalue of k .
Answer: By playing around, we find that Jarris should have his hypotenuse flat on the x -24
axis. The desired minimum value of k is then the length of the altitude to the hypotenuse. Thus, by 5
1 1 24
computing the area of the triangle in two ways, · 10 · k = · 6 · 8 and so k = .
2 2 5