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In the triangle below, AB = 3, AC= 6.[img]2022m10s/ct_ve01203002j_egreqbj_0001_
In the triangle below, AB = 3, AC= 6.[img]2022m10s/ct_ve01203002j_egreqbj_0001_
游客
2025-02-23
21
管理
问题
In the triangle below, AB = 3, AC= 6.
Quantity A: The area of triangle ABC
Quantity B: 10
选项
A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.
答案
B
解析
现在,即使考虑到点B是可以动的,但点B的位置也受题目中给出的条件限制。我们假设点A和点C是不动的,那么B可能存在的位置是一个以A为圆心,以AB长度为半径的圆上,如下图所示。不难得知,△ABC的面积存在最大值,在以AC为底边,当日点向下移(见下图),此三角形取到面积的最大值(从B向AC作的高最大),最大面积为(1/2)×3 × 6=9。所以即使在△ABC取到最大面积时,Quantity A依然小于Quantity B。因此,这道题的答案就不再是D,而变为B。
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