1.

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Answer»

❤\huge \bold \pink {Answer❤}

All the sides of the quadrilateral are equal. hence the quadrilateral is a rhombus.

Each side of the rhombus = 60 cm

Let ∠A=60

∘

Then, ∠C=∠A=60 (Opposite ANGLES)

and, ∠B=∠D=x

Sum of angles of rhombus = 360

∠A+∠B+∠C+∠D=360

2x=360−120

x=120

∘

∠B=∠D=120

∘

In △ABC

cosB=

2×AB×BC

AB

2

+BC

2

−AC

2

cos120=

2×60×60

60

2

+60

2

−AC

2

2

−1

=

2×60×60

60

2

+60

2

−AC

2

−60

2

=2×60

2

−AC

2

AC=60

3

AC=103.92 cm

In △ABD

∠A=60

∘

COSA=

2×AB×AD

AB

2

+AD

2

−BD

2

cos60=

2×60×60

60

2

+60

2

−BD

2

2

1

2×60×60

2×60

2

−BD

2

60

2

=2×60

2

−BD

2

BD=60 cm


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