It is currently 02 Apr 2020, 21:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:
Intern
Joined: 21 Apr 2019
Posts: 17
Followers: 0

Kudos [?]: 8 [2] , given: 5

In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink]  30 Jul 2019, 05:00
2
KUDOS
00:00

Question Stats:

66% (01:35) correct 33% (00:02) wrong based on 3 sessions
In 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) $$\sqrt{136}$$

E) 12 units

Source: Jamboree Green Book 1
[Reveal] Spoiler: OA
Intern
Joined: 06 Jul 2018
Posts: 6
Followers: 0

Kudos [?]: 8 [2] , given: 4

Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink]  10 Aug 2019, 22:51
2
KUDOS
Area = 60

0.5(AB + CD)(10) = 60
AB + CD = 12

From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10

Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)

Attachments

Trapezium.png [ 12.29 KiB | Viewed 533 times ]

Intern
Joined: 21 Apr 2019
Posts: 17
Followers: 0

Kudos [?]: 8 [0], given: 5

Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink]  11 Aug 2019, 05:49
Vyshak wrote:
Area = 60

0.5(AB + CD)(10) = 60
AB + CD = 12

From the below figure, we have
CD = EF = x
AB = 12 - x
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10

Triangle DEB is right angled --> BD^2 = 100 + 36 = 136
BD = sqrt(136)

Could u elaborate from :
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Intern
Joined: 06 Jul 2018
Posts: 6
Followers: 0

Kudos [?]: 8 [2] , given: 4

Re: In trapezium ABCD, AB||CD and AC = BD. If area of the [#permalink]  12 Aug 2019, 09:20
2
KUDOS
AB + CD = 12

If CD = x, AB = 12 - x

CD = EF = x

AE + FB = AB - EF = 12 - x - x = 12 - 2x

But AE = FB as the two triangles CAB and ADB are congruent(Side Angle Side).

Since AE = FB, AE + AE = 2AE = 12 - 2x --> AE = 6 - x

FB = 6 - x

Bijesh wrote:
Could u elaborate from :
AE = FB = (12-2x)/2 = 6 - x (Since AC = BD, the two triangles are similar)
EB = 6 - x + x = 6
BE = 10
Re: In trapezium ABCD, AB||CD and AC = BD. If area of the   [#permalink] 12 Aug 2019, 09:20
Display posts from previous: Sort by