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
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
3=(97-shorter base)/2 Multiply both side by 2
shorter base= 97-6
shorter base= 91
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