Question

In the given trapezium. ABCD , M and N are mid points of non parallel sides AD and BC. Find (i) MN if AB = 11 cm and DC = 8cm (ii) AB if DC =20cm and MN = 27 cm​

Answer 1

Step-by-step explanation:

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Answer 2

Cᴏɴsᴛʀᴜᴄᴛɪᴏɴ -

Join DB.

Sᴏʟᴜᴛɪᴏɴ -

i) MN , if AB = 11 cm and DC = 8 cm.

=> AB || DC,

M and N are the midpoints of sides AD and BC respectively.

∴ MN || AB and MN || DC.

Now,

OM = 1/2 AB [mid point theorem]

=> 1/2 × 11

=> 11/2

=> 5.5 cm

And,

ON = 1/2 DC [mid point theorem]

=> 1/2 × 8

=> 4 cm.

∴ MN = OM + ON

=> MN = 5.5 + 4

=> MN = 9.5 cm ..(ans)

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ii) AB, if DC = 20 cm and MN = 27 cm.

=> Let AB = x.

We know that,

MN = 1/2 (AB + DC)

=> 27 = 1/2 (x+20)

=> 27×2 = x + 20

=> 54 - 20 = x

∴ x = 34 cm ..(ans)

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iii) DC, if MN = 15 cm and AB = 23 cm.

=> Let DC = x.

we know that,

MN = 1/2 (AB + DC)

=> 15 = 1/2 (23+x)

=> 15×2 = 23+x

=> 30-23 = x

∴ x = 7 cm ..(ans)

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@MissSolitary✌️

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