Question

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

• A. $94$
• B. $92$
• C. $91$
• D. $90$
• E. $89$

Answer 1

Answer: (C)

$91$

The line segment joining the midpoints of diagonals of the trapezoid is parallel to the parallel sides and equal to half their difference.

$\therefore \frac{longerbase-shorterbase}{2}=3$

$\Rightarrow \frac{97-x}{2}=3\Rightarrow x=97-6=91$