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Question
The figure, given below, shows a trapezium ABCD. M and N are the mid-point of the non-parallel sides AD and BC respectively. Find:
- MN, if AB = 11 cm and DC = 8 cm.
- AB, if DC = 20 cm and MN = 27 cm.
- DC, if MN = 15 cm and AB = 23 cm.
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Solution
Let we draw a diagonal AC as shown in the figure below,
(i) Given that AB = 11 cm, CD = 8 cm
From triangle ABC
ON = `[1]/[2]` AB
= `[1]/[2]` × 11
= 5.5 cm
From triangle ACD
OM = `[1]/[2]` CD
=`[1]/[2]` × 8
= 4 cm
Hence, MN = OM + ON
= (4 + 5.5)
= 9.5 cm
(ii) Given that CD = 20 cm, MN = 27 cm
From triangle ACD
OM = `[1]/[2]` CD
= `[1]/[2]` × 20
= 10 cm
Therefore, ON = 27 - 10 = 17 cm
From triangle ABC
AB = 2ON
= 2 × 17
= 34 cm
(iii) Given that AB = 23 cm, MN = 15 cm
From triangle ABC
ON =`[1]/[2]` AB
=`[1]/[2]` × 23
= 11.5 cm
OM = 15 - 11.5
OM = 3.5 cm
From triangle ACD
CD = 2OM
= 2 × 3.5
CD = 7 cm
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