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# In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area

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SVP
Joined: 20 Jul 2017
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Location: India
Concentration: Entrepreneurship, Marketing
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In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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17 Jul 2019, 03:39
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In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area of ABCD? (in unit$$^2$$)

A. $$3\sqrt{3}/8$$
B. $$3\sqrt{3}/4$$
C. $$3\sqrt{3}/2$$
D. $$3\sqrt{3}$$
E. $$6\sqrt{3}$$
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Joined: 19 Oct 2018
Posts: 1987
Location: India
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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17 Jul 2019, 18:02
1
In triangle ABC
$$\frac{AB}{sin30}$$=$$\frac{AC}{sin120}$$
AB=$$\sqrt{3}$$

Area=$$AB^2 sin120$$ = $$\sqrt{3}^2*\sqrt{3}/2$$= $$3\sqrt{3}/2$$

Dillesh4096 wrote:
In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area of ABCD? (in unit$$^2$$)

A. $$3\sqrt{3}/8$$
B. $$3\sqrt{3}/4$$
C. $$3\sqrt{3}/2$$
D. $$3\sqrt{3}$$
E. $$6\sqrt{3}$$
Senior Manager
Joined: 10 Dec 2017
Posts: 278
Location: India
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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17 Jul 2019, 04:26
2
Dillesh4096 wrote:
In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area of ABCD? (in unit$$^2$$)

A. $$3\sqrt{3}/8$$
B. $$3\sqrt{3}/4$$
C. $$3\sqrt{3}/2$$
D. $$3\sqrt{3}$$
E. $$6\sqrt{3}$$

Rhombus:
1.Diagonals are perpendicular bisector of each other.
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
Intern
Joined: 11 May 2019
Posts: 19
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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08 Aug 2019, 03:07
Got it buy 30-60-90 triangle. Where am i wrong?

Posted from my mobile device
Manager
Joined: 20 Apr 2019
Posts: 112
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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14 Aug 2019, 00:47
satya2029 wrote:
Dillesh4096 wrote:
In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area of ABCD? (in unit$$^2$$)

A. $$3\sqrt{3}/8$$
B. $$3\sqrt{3}/4$$
C. $$3\sqrt{3}/2$$
D. $$3\sqrt{3}$$
E. $$6\sqrt{3}$$

Rhombus:
1.Diagonals are perpendicular bisector of each other.
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

Can someone please help on how to get from 3/2 (60°) to square root 3/2 (30°)? For the 30-60-90 Triangle
Intern
Joined: 31 Oct 2018
Posts: 7
Location: India
GMAT 1: 680 Q46 V38
GPA: 4
WE: Operations (Transportation)
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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06 Sep 2019, 02:10
1
Can someone please help on how to get from 3/2 (60°) to square root 3/2 (30°)? For the 30-60-90 Triangle[/quote]

30-60-90 Right angle Triangle Rule: Sides will be in Ratio. x:x√3:2.

Now as angle P is 90 degree and in triangle ABP angle B is 60 degree and angle A is 30 degrees, We can use the Ratios and Find out that side PB is √3/2.
SVP
Joined: 24 Nov 2016
Posts: 1663
Location: United States
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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10 Mar 2020, 12:15
Dillesh4096 wrote:
In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area of ABCD? (in unit$$^2$$)

A. $$3\sqrt{3}/8$$
B. $$3\sqrt{3}/4$$
C. $$3\sqrt{3}/2$$
D. $$3\sqrt{3}$$
E. $$6\sqrt{3}$$

area=d_1*d_2/2
ac=diagonal_1=3
bd=diagonal_2=?

dcb=(360-240)/2=60, opposite dab=60

perpendicular from d_1 to abc forms a right triangle
30-60-90 x:x√3:2x
x√3 is half d_1, x√3=3/2, x=3/2√3=√3/2
x is half d_2, so twice x is d_2=2√3/2=√3

area=3*√3/2

Ans (C)
Manager
Joined: 30 Jun 2019
Posts: 223
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area  [#permalink]

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10 Mar 2020, 14:54
The main trick here is to know that 3/2√3=√3/2
The rest is a pretty basic 30-60-90 triangle.

3/2√3:3/2:3/√3

2*(3/2√3*3/2) = 9/2√3 = 3√3/2
Re: In a rhombus ABCD, AC = 3 units and angle ABC = 120°. What is the area   [#permalink] 10 Mar 2020, 14:54