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# In triangle ABC angle ABC is 90 degrees. What is the

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In triangle ABC angle ABC is 90 degrees. What is the [#permalink]

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11 Oct 2008, 06:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

a:ab+bc=7
b: ab/bc =3/4

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

A alone is not sufficient? as it is right angle triangle and B is 90..means AB and BCmust be 3 and 4 or 4 and 3?

Thanks
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 06:08
C

perimeter = ab + bc +ac

1. ab+bc = 7
can't find ac
Not sufficient

2. ab/bc = 3/4
can't find ac
Not sufficient

Together : we can get ac
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 06:11
vishalgc wrote:
In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

a:ab+bc=7
b: ab/bc =3/4

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

A alone is not sufficient? as it is right angle triangle and B is 90..means AB and BCmust be 3 and 4 or 4 and 3?

Thanks

A is not suff. It can be 1+6 , 2+5, 3+4
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 07:35
1
KUDOS
Hey here they have specify that its right angle trinagle..

so its side must be in 3:4:5 ratio..

Now they say ab+bc = 7 and only one combination is possible.. (3-4 or 4-3) so third one will be def. 5

So I think A is enough.

Thanks
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 08:52
Vishal: I think you are right

+1 for you
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 08:55
vishalgc wrote:
Hey here they have specify that its right angle trinagle..

so its side must be in 3:4:5 ratio..

Now they say ab+bc = 7 and only one combination is possible.. (3-4 or 4-3) so third one will be def. 5

So I think A is enough.

Thanks

Hey !! Yes you are right Vishal
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 09:30
vishalgc wrote:
Hey here they have specify that its right angle trinagle..

so its side must be in 3:4:5 ratio..

Now they say ab+bc = 7 and only one combination is possible.. (3-4 or 4-3) so third one will be def. 5

So I think A is enough.

Thanks

Vishal from where you get the relation between 3 sides of Rt Angled Triangle 3:4:5, is it always true ? I dont think so?

For me you can get ans of this quest by considering both the statements.
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 10:18
I don't think A is sufficient.

Vishal I think you may want to check again with the ratio 3:4:5. As I remember, a triangle that has its sides with ratio 3:4:5 usually could be right triangle. This is often used as a tip to solve the difficult calculation of sides' lengths rather than a definition of right triangle.

Given AB=2, BC=5, then according to Pithagor formular, we will have AC=sqrt(AB^2+BC^2)=sqrt29. We quite can draw such a triangle.

IMO C.
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 10:25
I don't think A is sufficient.

Vishal I think you may want to check again with the ratio 3:4:5. As I remember, a triangle that has its sides with ratio 3:4:5 usually could be right triangle. This is often used as a tip to solve the difficult calculation of sides' lengths rather than a definition of right triangle.

Given AB=2, BC=5, then according to Pithagor formular, we will have AC=sqrt(AB^2+BC^2)=sqrt29. We quite can draw such a triangle.

IMO C.

My Vote is with you !!
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 12:44
I get A too..

this is a 3:4:5 triangle, these are well-known like 5-12-13..memorize them
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 13:08
I think Vishal is right here...

Right angled traingle can have any of these ratios for sides
1:1:sqrt(2)
1:sqrt(3):2
3:4:5
5:12:13
8:15:17 etc

Based on statement 1 :
since side 1+ side 2 = 7, we can easily assume 2 of the sides as 3 and 4, so the 3rd has to be 5
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 19:57
Guys.. Why cant side 1 + side 2 = 7 be 1 + 6 = 7 ?? The third side will be 1^2 + 6^2 = 37

the third side can be SQRT(37). So what if the third side is not a positive integer ?? Pythogoras theorem does not mandate that all three sides are integers.
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Re: perimeter of the triangle ABC? [#permalink]

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11 Oct 2008, 21:08
vishalgc wrote:
In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

a: ab+bc=7
b: ab/bc =3/4

A alone is not sufficient? as it is right angle triangle and B is 90..means AB and BCmust be 3 and 4 or 4 and 3?

Thanks

C.

St. 1 would be suff if angles were in the ratio of 30:60:90. do we know the measure of other 2 angles? no. so insuff.
St. 2 is same as st. 1.

so only togather, we know the sides ab and bc and then ca and perimeter....

If A is suff, the right angle means only 30:60:90 where as in fact, there are infinite ways a right angle triangle can be drawn....
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Re: perimeter of the triangle ABC? [#permalink]

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12 Oct 2008, 10:45
GMAT TIGER wrote:
vishalgc wrote:
In triangle ABC angle ABC is 90 degrees. What is the perimeter of the triangle ABC?

a: ab+bc=7
b: ab/bc =3/4

A alone is not sufficient? as it is right angle triangle and B is 90..means AB and BCmust be 3 and 4 or 4 and 3?

Thanks

C.

St. 1 would be suff if angles were in the ratio of 30:60:90. do we know the measure of other 2 angles? no. so insuff.
St. 2 is same as st. 1.

so only togather, we know the sides ab and bc and then ca and perimeter....

If A is suff, the right angle means only 30:60:90 where as in fact, there are infinite ways a right angle triangle can be drawn....

Agreed with GMAT tiger !!there are infinite combinations !!!

consider equations

1)ab+bc=7 ab bc can be fractions too !!!hence the values can be any

again consider
2) ab/bc =3/4 this can also led to multiple set of values !!

IMO C ,combine solve get the values then get third side
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Re: perimeter of the triangle ABC?   [#permalink] 12 Oct 2008, 10:45
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