|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 24 Jul 2009
Posts: 197
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4
Kudos [?]:
17
[0], given: 10
|
If angle BAD is a right angle, what is the length of side [#permalink]
 23 Jan 2010, 16:43
Question Stats:
66% (02:36) correct
33% (00:35) wrong based on 1 sessions
If angle BAD is a right angle, what is the length of side BD? (1) AC is perpendicular to BD (2) BC = CD Source MGMAT Geometry Question Bank From (2), can I automatically infer that AC is a bisector? OPEN DISCUSSION OF THIS QUESTION IS HERE: if-angle-bad-is-a-right-angle-what-is-the-length-of-side-105559.html
Attachments
triangleABCD.jpg [ 23.6 KiB | Viewed 1419 times ]
_________________
Reward wisdom with kudos. 
|
|
|
|
|
|
|
|
|
Manager
Joined: 24 Jul 2009
Posts: 197
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4
Kudos [?]:
17
[0], given: 10
|
Re: What is the hypotenuse? [#permalink]
23 Jan 2010, 16:50
How is BAD an isoceles triangle? I do not understand MGMAT's explanation.
_________________
Reward wisdom with kudos.
|
|
|
|
|
|
Senior Manager
Joined: 21 Jul 2009
Posts: 371
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 11
Kudos [?]:
74
[1] , given: 22
|
Re: What is the hypotenuse? [#permalink]
23 Jan 2010, 17:13
1
This post received
KUDOS
gottabwise wrote: If angle BAD is a right angle, what is the length of side BD? (1) AC is perpendicular to BD (2) BC = CD Source MGMAT Geometry Question Bank From (2), can I automatically infer that AC is a bisector? From the given figure, when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD. When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way. When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5.
_________________
I am AWESOME and it's gonna be LEGENDARY!!!
|
|
|
|
|
|
Manager
Joined: 24 Jul 2009
Posts: 197
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4
Kudos [?]:
17
[0], given: 10
|
Re: What is the hypotenuse? [#permalink]
23 Jan 2010, 20:18
BarneyStinson wrote: gottabwise wrote: If angle BAD is a right angle, what is the length of side BD? (1) AC is perpendicular to BD (2) BC = CD Source MGMAT Geometry Question Bank From (2), can I automatically infer that AC is a bisector? From the given figure, when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD. When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way. When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5. Thank you for the clear explanation. It helped a great deal.
_________________
Reward wisdom with kudos.
|
|
|
|
|
|
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 551
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 1
Kudos [?]:
13
[0], given: 560
|
Re: If angle BAD is a right angle, what is the length of side [#permalink]
24 Jan 2013, 07:21
Hi Bunuel/Karishma I still don't understand how BAD is an isoceles triangle? Kindly help..
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595
My GMAT Journey : end-of-my-gmat-journey-149328.html#p1198742
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11519
Followers: 1795
Kudos [?]:
9546
[0], given: 826
|
Re: If angle BAD is a right angle, what is the length of side [#permalink]
24 Jan 2013, 07:24
|
|
|
|
|
|
|
Re: If angle BAD is a right angle, what is the length of side
[#permalink]
24 Jan 2013, 07:24
|
|
|
|
|
|
|
|
|
|
|
close
