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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: 120
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, 13:03
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55% (hard)

Question Stats:

64% (02:11) correct 36% (01:40) wrong based on 44 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 BC?

(A) 10 units

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

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

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

(E) 12 units
[Reveal] Spoiler: OA
Senior Manager
Joined: 31 Jul 2017
Posts: 342
Location: Malaysia
WE: Consulting (Energy and Utilities)
In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink]

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04 Feb 2018, 14:24
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 = $$\frac{1}{2}h(a+b)$$
$$a, b = Length of parallel sides.$$
$$h = Height between the two parallel sides.$$
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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, 22:28
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
Senior Manager
Joined: 31 Jul 2017
Posts: 342
Location: Malaysia
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, 22:37
1
KUDOS
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, 12:48
Thanks! I thought it was an assumption not a solution

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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6   [#permalink] 08 Feb 2018, 12:48
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