The longer base of a trapezoid is 97. The line segment joining the midpoints of the diagonals is 3. Find the measure of the shorter base Clarification: the two diagonals have midpoints  that don't...

The longer base of a trapezoid is 97. The line segment joining the midpoints of the diagonals is 3. Find the measure of the shorter base

Clarification: the two diagonals have midpoints  that don't necessarily intersect. The two midpoints are joined by a line spanning the space inbetween them.

97 and 3 are measurements (I had too many characters to say that)

Our teacher gave us this for fun, and it's really been bugging me

Expert Answers
hala718 eNotes educator| Certified Educator

The segment joining the midpoints of the two diagonals is parallel to the bases and equal to one half of the difference of the bases.

A = longer base

B = shorter base

the segment = (A - B) / 2

3 = (97 - B) / 2

6 = 97 - B

B = 97 - 6 = 91

Jyotsana | Student

3=(97-shorter base)/2    Multiply both side by 2

6=97-shorter base

shorter base= 97-6

shorter base= 91

revolution | Student

1/2 ( longer base- shorter base)= segment joining the two midpts.

1/2( 97- shorter base) =3

Multiply both side by 2

97- shorter base=6

shorter base= 91cm