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Question

ABCD is the parallelogram and E, F, G and H are the midpoints of sides AB, BC, CD and DA respectively. EF=6 cm and perimeter of EFGH is 18 cm. Find the length of diagonal BD.

A
3 cm
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B
6 cm
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C
9 cm
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D
12 cm
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Solution

The correct option is B 6 cm
We know the midpoints of sides of parallelogram when joined to form quadrilateral, they form a parallelogram
So, EFGH is parallelogram.
SoEF=HG and HE=GF (pair of opposite sides of parallelogram)
EF=HG=6cm
let HE=GF=x
Now,
Perimeter of EFGH=EF+FG+GH+HE
18=6+6+x+x
2x+12=18
2x=1812
2x=6
x=62
x=3 cm

means HE=3 cm.
Now drawn diagonal BD

In ABD
H and E are midpoints of sides AD and AB respectively so line joining H and E will be half of its parallel side i.e. BD by mid point theorem.

So, HE=BD2
3=BD2
BD=3×2
BD=6 cm

Hence, diagonal BD=6 cm.
So, option (b) correct.

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