SOLUTION: How do I know what kind of triangle it will form from it's length measurements? Acute, Right, or Obtuse? 1) 4cm, 4cm, 4cm 2) 3cm, 4cm, 5cm 3) 5cm, 11cm, 12cm

Algebra ->  Algebra  -> Triangles -> SOLUTION: How do I know what kind of triangle it will form from it's length measurements? Acute, Right, or Obtuse? 1) 4cm, 4cm, 4cm 2) 3cm, 4cm, 5cm 3) 5cm, 11cm, 12cm      Log On

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Question 146185: How do I know what kind of triangle it will form from it's length measurements? Acute, Right, or Obtuse?
1) 4cm, 4cm, 4cm
2) 3cm, 4cm, 5cm
3) 5cm, 11cm, 12cm
Answer by nabla(475) About Me  (Show Source):
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1. All sides are equal, thus by theorem all angles are equal. So 3s=180, s=60. This is acute.
2. Look at the Pythagorean Theorem. a^2+b^2=c^2. Do these sides fit? 3^2+4^2=9+16=25.. sqrt(25)=5, yes. Thus it must be a right triangle.
3. The inequality relation a%5E2%2Bb%5E2%3Cc%5E2 must be met if this is an obtuse triangle.
5^2+11^2=25+121=136<144. Thus it must be an obtuse triangle.