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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
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Solution
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.
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