Geometry:Right angle property

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zaarathelab: Master | Next Rank: 500 Posts; Posts: 217; Joined: Sun Jan 10, 2010 1:39 pmFollowed by: 1 member; Thanked: 7 times

by zaarathelab » Mon Dec 12, 2011 7:44 am

Pls see attachment.
If Triangle BAD is a right angle, what is the length of side BD?

1)AC is perpendicular to BD
2)BC = CD

Experts, need your comments

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 12, 2011 7:44 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Dec 12, 2011 8:17 am

Statement 1
AC perpendicular to BD
tells us nothing

Its insufficient

Statement 2
BC = CD

We have no clue what point C is..
Insufficient

Combining two statements ...
AC perpendicual to BD and BC= CD

triangle ACB and triangle ACD will be congruent
AB = AC = 5
BC = 5*rt(2)

Option C

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Dec 12, 2011 9:48 pm

zaarathelab wrote:Pls see attachment.
If Triangle BAD is a right angle, what is the length of side BD?

1)AC is perpendicular to BD
2)BC = CD

Experts, need your comments

(1) AC is perpendicular to BD does not help us to find the length of BD; NOT sufficient.

(2) BC = CD
Triangles ACB and ACD are congruent to each other, as BC = CD, AC = AC(common). Since the two triangles are congruent, so AB = AD = 5. BAD is right angled at A, so by Pythagoras Theorem, we can find BD; SUFFICIENT.

The correct answer is B.

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zaarathelab: Master | Next Rank: 500 Posts; Posts: 217; Joined: Sun Jan 10, 2010 1:39 pmFollowed by: 1 member; Thanked: 7 times

by zaarathelab » Tue Dec 13, 2011 12:43 am

OA is C

Anurag, can you pls illustrate the relationships in this special type of right angled triangle with respect to:
1. AC is perpendicular to BD
2. AC is a median
3. AC is a perpendicular bisector of BD

My take

1. AC is perpendicular to BD MEANS AC^2 = BC*CD (All triangles are similar)
2. AC is a median MEANS BC=CD and all triangles are similar (BA=BC) ABD is an isoceles triangle (AD=AB)
3. AC is the perpendicular bisector of BD MEANS BC=CD and all triangles are similar (BA=BC) ABD is an isoceles triangle (AD=AB)

I often get confused with this type of triangle

Thanks

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