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If three sides of a triangle measure a, b, c, is triangle ABC a right

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If three sides of a triangle measure a, b, c, is triangle ABC a right  [#permalink]

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New post 25 Feb 2019, 08:44
2
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

43% (01:05) correct 57% (01:14) wrong based on 30 sessions

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If three sides of a triangle measure a, b, c, is triangle ABC a right angle triangle?

1. \(a^2\) + \(b^2\) < 25

2. c>5

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Re: If three sides of a triangle measure a, b, c, is triangle ABC a right  [#permalink]

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New post 25 Feb 2019, 12:28
fitzpratik wrote:
If three sides of a triangle measure a, b, c, is triangle ABC a right angle triangle?

1. \(a^2\) + \(b^2\) < 25

2. c>5


This question is one where you can almost go straight to looking at the statements together. A right triangle is one where the three sides can be related to each other by the equation (side1)^2 + (side2)^2 = (hypotenuse)^2. Therefore, we need to know something about all 3 sides.

Statement 1) Tells nothing about c----> insufficient

Statement 2) Tells nothing about a&b ---> insufficient

1&2 Together)
- If a^2 + b^2 is less than 25 than each of a^2 and b^2 must also be less than 25. Therefore, a < 5 and b < 5.
- If c > 5 then we know it is longer than a & b. Therefore, if we wanted to try and make a right triangle out of these sides c would have to be the hypotenuse and c^2 is greater than 25
- Try to come up with examples where a^2 + b^2 = c^2
- From what we know from before --->a^2 + b^2 = c^2-----> is same as saying -----> Some Number Less Than 25 = Some Number Greater Than 25.

This is not possible therefore it is SUFFICIENT to say this is NOT a right triangle

Answer: C
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Re: If three sides of a triangle measure a, b, c, is triangle ABC a right   [#permalink] 25 Feb 2019, 12:28
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