find the lengths of diagonals AC and BD Given AB =60cm and angel BAD=60
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Step-by-step explanation:
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
hope you like this answer.
thanks
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