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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
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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
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