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

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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   04 Feb 2018, 13:03
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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
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   06 Jun 2018, 20:50
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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)
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   04 Feb 2018, 14:24
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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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   07 Feb 2018, 22:37
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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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   03 Oct 2019, 12:43
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Instead of doing so much calculation, just assume that the trapezium is rectangle with area equal to 60sqm and height equal to 10m. Since there is no condition given for the 2 parallel sides, hence our assumption should not affect the solution.
With this method the question could be solved in hardly 30seconds.
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   06 Jun 2018, 17:30
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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
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   18 Jun 2018, 17:17
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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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   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
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   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] New post   08 Jun 2018, 03:01
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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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 [#permalink] New post   18 Jun 2018, 20:05
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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] New post   20 Aug 2022, 03:58
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