ABCD is a quadrilateral in which AB ∥ DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 74 cm, BC = 91 cm, DC = 26 cm, and AD = 39 cm, then what is the length (in cm) of EF?
24
Since AB ∥ DC, the quadrilateral ABCD is a trapezium with AB and DC as its two parallel sides.
There is a standard result: the segment joining the mid points of the diagonals of a trapezium is parallel to the parallel sides and equals half the difference of those parallel sides.
So \(EF=\frac{1}{2}\,|AB-DC|\).
Substituting the parallel-side lengths: \(EF=\frac{1}{2}(74-26)=\frac{48}{2}=24\) cm. (The non-parallel sides BC and AD do not affect this length.)
Hence, the length of EF is 24 cm.
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