1959 AMC 12 第 22 题

Question

连接一个梯形两条对角线中点的线段长为

3

。若较长的底边长为

97

，则较短的底边长为：

The line joining the midpoints of the diagonals of a trapezoid has length

3.

If the longer base is

97,

then the shorter base is:

94

92

91

90

89

知识点：梯形中点

回忆梯形两条对角线中点连线的长度

Recall the length of the segment joining the diagonal midpoints of a trapezoid

它等于两底边长度之差的一半

It equals half the difference of the base lengths

若较短底边为

b

，则对角线中点连线的长度为两底边之差的一半：

\frac{97-b}{2}=3\text{。}

因此

97-b=6

，且

b=91

。

因此，正确答案是 C。

If the shorter base is

b,

the diagonal-midpoint segment has length half the difference of the bases:

\frac{97-b}{2}=3.

Thus

97-b=6

and

b=91.

Therefore, the correct answer is C.

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