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by diebeatsthegmat » Fri Jul 15, 2011 12:43 am
What is the perimeter of the isoceles right triangle ABC

S1 AB = 9

S2 BC = 4

i dont understand why the answer is C since we dont know which sides are equal
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Source: — Data Sufficiency |
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by pemdas » Fri Jul 15, 2011 1:16 am
my answer is e
st(1) AB=9 and AB can be either hypotenuse or non-hypotenuse side, Not Sufficient
st(2) BC=4 the same applies as for st(1), Not Sufficient
combined st(1&2) the hypotenuse should be longer than non-hypotenuse side, hence hypotenuse is 9 and non-hypotenuse sides are 4, which is not possible as 2*(4^2) will return 32 and not 81 (or 9^2) Not Sufficient.

If this question would be rephrased to only right triangle (not isosceles right triangle) then the answer would be c
diebeatsthegmat wrote:What is the perimeter of the isoceles right triangle ABC

S1 AB = 9

S2 BC = 4

i dont understand why the answer is C since we dont know which sides are equal
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by Ian Stewart » Fri Jul 15, 2011 7:46 am
If the sides of a triangle are a, b and c, it is always true that the sum of any two sides of the triangle must exceed the third side - that is, that

a + b > c
a + c > b
b + c > a


So with both statements together, it's certainly possible for the three sides to be 9, 9 and 4. It is not, however, possible for the sides to be 4, 4 and 9, since 4+4 is not greater than 9. So the answer is C.
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by rahulvsd » Fri Jul 15, 2011 8:20 am
Hi Ian,

Yes, it is possible to form a triangle using both the statements, but the answer should be E in this case as the question states that the given sides form an isosceles right triangle and it is not possible to form an isosceles right triangle with 9,9 and 4. Please correct me if I am worng.
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by Frankenstein » Fri Jul 15, 2011 8:26 am
pemdas wrote: If this question would be rephrased to only right triangle (not isosceles right triangle) then the answer would be c
Hi,
No, Even if it is rephrased to right triangle, the answer is E, because if 4,9 are two sides, third side can be either sqrt(9^2 - 4^2) or sqrt(9^2+4^2).
The answer would be C if the triangle given is isosceles(not isosceles right triangle) because third side cannot be 4(as 4+4<9). It can only be 9.
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by diebeatsthegmat » Fri Jul 15, 2011 8:55 am
Ian Stewart wrote:If the sides of a triangle are a, b and c, it is always true that the sum of any two sides of the triangle must exceed the third side - that is, that

a + b > c
a + c > b
b + c > a


So with both statements together, it's certainly possible for the three sides to be 9, 9 and 4. It is not, however, possible for the sides to be 4, 4 and 9, since 4+4 is not greater than 9. So the answer is C.
ahh yeah... i should pay more attention while learning... thank you
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by Frankenstein » Fri Jul 15, 2011 9:01 am
diebeatsthegmat wrote: ahh yeah... i should pay more attention while learning... thank you
Hey,
Please check the source from which this question is posted. Are you sure it is isosceles right triangle or just isosceles triangle?
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by Ian Stewart » Fri Jul 15, 2011 12:34 pm
rahulvsd wrote:Hi Ian,

Yes, it is possible to form a triangle using both the statements, but the answer should be E in this case as the question states that the given sides form an isosceles right triangle and it is not possible to form an isosceles right triangle with 9,9 and 4. Please correct me if I am worng.
Good point - I've seen so many questions like this one before, I just glossed over the word 'right' in the question. If the question asks about an 'isosceles right triangle', the question doesn't make any sense, since it's impossible to construct an isosceles right triangle with the dimensions given. So I'm sure the question means to ask just about "isosceles triangle ABC", and not about "isosceles right triangle ABC".
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