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In a rhombus ABCD , AC= 3 units and angle ABC = 120' ,
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27 Jul 2019, 03:38
27 Jul 2019, 03:38
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Question Stats:
66% (09:10) correct
33% (05:32) wrong based on 3 sessions
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In a rhombus ABCD , AC= 3 units and angle ABC = 120' , What is the area of ABCD? (in unit square)
A) \(3\sqrt{3} / 8\)
B) \(3\sqrt{3} / 4\)
C) \(3\sqrt{3} / 2\)
D) \(3\sqrt{3}\)
E) \(6\sqrt{3}\)
Source : Gre Book 1 from Jamboree
A) \(3\sqrt{3} / 8\)
B) \(3\sqrt{3} / 4\)
C) \(3\sqrt{3} / 2\)
D) \(3\sqrt{3}\)
E) \(6\sqrt{3}\)
Source : Gre Book 1 from Jamboree
Re: In a rhombus ABCD , AC= 3 units and angle ABC = 120' ,
[#permalink]
27 Jul 2019, 04:18
27 Jul 2019, 04:18
1
Expert Reply
1.Diagonals are perpendicular bisector of each other.
2. Adjacent angles are supplementary.
AC= 3
Diagonals bisect each other at P(say) AC, BD
AP+PC=AC
AP= 3/2
IN TRIANGLE -ABP
As adjacent angles are supplementary angle
angle at A= 60
angle ABC=120
as Diagonals are perpendicular bisector of each other
in triangle ABP( 30-60-90)
We know AP=3/2
BP=square root 3/2
area= (AC X BD)/2
=(3 X 2 BP)/2
= 3 square root 3/2
C
2. Adjacent angles are supplementary.
AC= 3
Diagonals bisect each other at P(say) AC, BD
AP+PC=AC
AP= 3/2
IN TRIANGLE -ABP
As adjacent angles are supplementary angle
angle at A= 60
angle ABC=120
as Diagonals are perpendicular bisector of each other
in triangle ABP( 30-60-90)
We know AP=3/2
BP=square root 3/2
area= (AC X BD)/2
=(3 X 2 BP)/2
= 3 square root 3/2
C
gmatclubot
Re: In a rhombus ABCD , AC= 3 units and angle ABC = 120' , [#permalink]
27 Jul 2019, 04:18
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