Question

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm? 1. acute, because 62 + 102 < 122 2.acute, because 6 + 10 > 12 3.obtuse, because 62 + 102 < 122 4.obtuse, because 6 + 10 > 12

Answer 1

Answer:

The best represents a triangle is obtuse, because 6 + 10 > 12 ⇒ answer 4

Step-by-step explanation:

* Lets talk about some facts in the triangle

- The triangle is formed when the sum of the lengths of the shortest

 two side is greater then the length of the longest side

∵ The lengths of the sides are 6 cm , 10 cm , 12 cm

∵ 6 + 10 > 12

∴ 6 , 10 , 12 are the sides of a triangle

- Two know the type of the triangle use these rules

# The three sides of the triangle have lengths a , b , c where a and b

  are the shortest sides means a , b < c, then

- If a² + b² > c² , the triangle is acute triangle (its 3 angles are acute)

- If a² + b² = c² , the triangle is right triangle (the angle opposite to c is a

 right angle and the other 2 angles are acute angles)

- If a² + b² < c² , the triangle is obtuse triangle (the angle opposite to c is an

 obtuse angle and the other 2 angles are acute angles)

∵ (6)² + (10)² = 36 + 100 = 136

∵ (12)² = 144

∵ 136 < 144

∴ (6)² + (10)² < (12)²

∴ The triangle is obtuse

* The best represents a triangle is obtuse, because 6 + 10 > 12