Question

In the given figure, ABCD is a trapezium. P and Q are the midpoints of non-parallel side AD and BC respectively. Find: AB, if DC = 8 cm and PQ = 9.5 cm

Answer 1

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

Given DC = 8 cm and PQ = 9.5 cm
In ΔADC,

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

⇒ OP = `(1)/(2) xx 8` = 4 cm

Now, 
OQ = PQ - OP
⇒ OQ = 9.5 - 4
= 5.5 cm

In ΔABC,

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

⇒ AB = 2 x OQ
= 2 x 5.5
= 11 cm.