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Question

If ABCD is a parallelogram whose diagonals intersect at O and ΔBCD is an equilateral triangle having each side of length 6 cm, then the length of diagonal AC is ____ .

A
33 cm
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B
63 cm
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C
36 cm
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D
12 cm
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Solution

The correct option is B 63 cm
ABCD is a parallelogram.
BC=AD=6 cm
and AB=DC=6 cm,
Triangle BCD is equilateral triangle
then BD=6 cm
Hence ABCD becomes a rhombus.
∴ Diagonals AC and BD bisect each other at right angle.
OD=12BD=62=3 cm
ΔOCD
(OC)2=CD2(OD)2=(6)2(3)2=369=27
OC=33
AC=2×OC=2×33=63 cm

635101_371759_ans.png

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