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655-705 (Hard)|   Geometry|      
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DHAR
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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 04 Feb 2018, 13:03
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Difficulty:

65% (hard)

Question Stats:

62% (02:47) correct 38% (03:02) wrong based on 150 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
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D
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PKN
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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 06 Jun 2018, 20:50
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GMATSkilled
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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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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rahul16singh28
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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 04 Feb 2018, 14:24
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DHAR
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
Show more

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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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 07 Feb 2018, 22:28
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rahul16singh28
DHAR
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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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!


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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 07 Feb 2018, 22:37
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diamund223
rahul16singh28
DHAR
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!


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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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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 08 Feb 2018, 12:48
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Thanks! I thought it was an assumption not a solution

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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 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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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 08 Jun 2018, 03:01
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GMATSkilled
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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Merging topics. Please search before posting.
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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 18 Jun 2018, 17:17
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DHAR
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
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Hi, please correct this. It should be diagonal BD.
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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 18 Jun 2018, 20:05
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DHAR
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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In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 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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