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
