Question

In the given figure, ABCD is a trapezium. P and Q are the midpoints of non-parallel side AD and BC respectively. Find: DC, if AB = 20 cm and PQ = 14 cm

Answer 1

Let us draw a diagonal AC which meets PQ at O as shown below:

Given AB = 20 cm and PQ = 14 cm
In ΔABC,

OQ = `(1)/(2)"AB"`     ....(Mid-point Theorem)

⇒ OP = `(1)/(2) xx 20` = 10 cm

Now, 
OP = PQ - OQ
⇒ OP = 14 - 10
= 4 cm

In ΔADC,

OP = `(1)/(2)"DC"`    ....(Mid-point Theorem)

⇒ DC = 2 x OP
= 2 x 4 
= 8 cm.