Question

Let AD and BC be the parallel sides of a
trapezium ABCD. Let P and Q be the midpoints
of the diagonals AC and BD. If AD = 16 and
BC = 20, then what is the length of PQ ?​

Answer 1

Answer:

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refer the reference diagram uploaded above

Step-by-step explanation:

Given:

quadrilateral abcd is a trapezium

where ad=16 and bc=20 which are two parallel sides

now since p and q are midpoints of ac and bd

we can use here midpoint theorem

so according to midpoint theorem

line segment joining midpoints of two sides is parallel to third and half of it

thus pq is parallel to bc and pq is parallel to ad

moreover pq=1/2×ad and pq=1/2×bc

so thus pq=1/2×ad=1/2×bc

so pq=1/2×ad-1/2×bc=0

so that is

=1/2(ad-bc)

=1/2(16-20)

=1/2×(-4)

=-2

pq=-2=0

ie pq=2 units

hence length of pq is 2 units