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 B6 cm We know the midpoints of sides of parallelogram when joined to form quadrilateral, they form a parallelogram
So, EFGH is parallelogram.
SoEF=HGandHE=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=18−12 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.