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# In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6

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Manager
Joined: 15 Dec 2015
Posts: 115
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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04 Feb 2018, 12:03
1
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Difficulty:

65% (hard)

Question Stats:

63% (02:53) correct 37% (02:56) wrong based on 95 sessions

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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BD?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units
Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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04 Feb 2018, 13:24
DHAR wrote:
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BC?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units

Area of Trapezium = $$\frac{1}{2}h(a+b)$$
$$a, b = Length of parallel sides.$$
$$h = Height between the two parallel sides.$$
Attachments

New Doc 32_4.jpg [ 344.55 KiB | Viewed 2507 times ]

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Intern
Joined: 01 Nov 2011
Posts: 2
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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07 Feb 2018, 21:28
rahul16singh28 wrote:
DHAR wrote:
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BC?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units

Area of Trapezium = $$\frac{1}{2}h(a+b)$$
$$a, b = Length of parallel sides.$$
$$h = Height between the two parallel sides.$$

I can’t visualise how you got to b-x=6. Otherwise I just plug in numbers might fit, like a=4 tf b=8 Please help!

Sent from my iPhone using GMAT Club Forum mobile app
Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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07 Feb 2018, 21:37
2
diamund223 wrote:
rahul16singh28 wrote:
DHAR wrote:
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BC?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units

Area of Trapezium = $$\frac{1}{2}h(a+b)$$
$$a, b = Length of parallel sides.$$
$$h = Height between the two parallel sides.$$

I can’t visualise how you got to b-x=6. Otherwise I just plug in numbers might fit, like a=4 tf b=8 Please help!

Sent from my iPhone using GMAT Club Forum mobile app

Hi,

$$a + b = 12$$
$$a = b - 2x.$$. Substitute this in the above equation
We get, $$2(b-x) = 12 ---> b - x = 6$$
Hope, its clear.
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Intern
Joined: 01 Nov 2011
Posts: 2
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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08 Feb 2018, 11:48
Thanks! I thought it was an assumption not a solution

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Manager
Joined: 08 Apr 2017
Posts: 78
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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06 Jun 2018, 16:30
1
In a trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq. units, and height of the trapezium is 10 units, what is the length of diagonal BD?

A. 10 units

B. $$\sqrt{116}$$ units

C. 5$$\sqrt{5}$$ units

D. $$\sqrt{136}$$ units

E. 12 units
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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06 Jun 2018, 19:50
2
GMATSkilled wrote:
In a trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq. units, and height of the trapezium is 10 units, what is the length of diagonal BD?

A. 10 units

B. $$\sqrt{116}$$ units

C. 5$$\sqrt{5}$$ units

D. $$\sqrt{136}$$ units

E. 12 units

Kindly refer the affixed diagram,

Given AB||CD and BD=AC(diagonals), hence it's a isosceles trapezium. hence AM=BN.
ADM, BNC & DMB are right angled triangles.
Given area of trapezium=60 sq unit
Or, ½*10(AB+CD)=60
Or, AB+CD=12
Or, X+AM+X+BN=12
Or, 2X+2BN=12
Or, X+BN=6
Or, MB=6 unit
Applying Pythagoras theorem in the right angled triangle DMB, we have
$$BD^2$$=$$DM^2$$+$$MB^2$$=$$10^2$$+$$6^2$$=136
So, BD=$$\sqrt{136}$$ units
Ans Option (D)
Attachments

Trapezoid.JPG [ 18.15 KiB | Viewed 1826 times ]

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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08 Jun 2018, 02:01
GMATSkilled wrote:
In a trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq. units, and height of the trapezium is 10 units, what is the length of diagonal BD?

A. 10 units

B. $$\sqrt{116}$$ units

C. 5$$\sqrt{5}$$ units

D. $$\sqrt{136}$$ units

E. 12 units

Merging topics. Please search before posting.
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Manager
Joined: 08 Apr 2017
Posts: 78
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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18 Jun 2018, 16:17
1
DHAR wrote:
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BC?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units

Hi, please correct this. It should be diagonal BD.
Math Expert
Joined: 02 Sep 2009
Posts: 52905
Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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18 Jun 2018, 19:05
GMATSkilled wrote:
DHAR wrote:
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units, height of the trapezium is 10 units, what is the length of diagonal BC?

(A) 10 units

(B) $$\sqrt{116}$$ units

(C) $$5\sqrt{5}$$ units

(D) $$\sqrt{136}$$ units

(E) 12 units

Hi, please correct this. It should be diagonal BD.

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Done. Thank you.
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6   [#permalink] 18 Jun 2018, 19:05
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