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.