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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]

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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]

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New post 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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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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!


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

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New post 07 Feb 2018, 22:37
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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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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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]

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New post 06 Jun 2018, 17:30
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
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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New post 06 Jun 2018, 20:50
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)
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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New post 08 Jun 2018, 03:01
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


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

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New post 18 Jun 2018, 17:17
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.
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6  [#permalink]

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New post 18 Jun 2018, 20:05
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 6 &nbs [#permalink] 18 Jun 2018, 20:05
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