Answer
2, 4, 5 (Obtuse Triangle)
3, 4, 5 (Right angle triangle)
6, 7, 8 (Acute Triangle)(
7, 9, 15 (Obtuse Triangle)
Step-by-step explanation
To answer this question, we first explain what these type of triangles are
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
If the three sides in a triangle are a, b and c with c being the longest side.
When
c² < a² + b²
The triangle is an acute triangle.
When
c² = a² + b²
The triangle is a right angle triangle.
When
c² > a² + b²
The triangle is an obtuse triangle.
But, it should be noted that if the longest side is equal to or more than the sum of the two sides, c ≥ a + b, the triangle is not possible.
So, taking these given side lengths one at a time,
2, 4, 5
a = 2, b = 4, c = 5
a² + b² = 2² + 4² = 4 + 16 = 20
c² = 5² = 25
25 > 20
c² > a² + b²
This triangle is an obtuse triangle.
3, 4, 5
a = 3, b = 4, c = 5
a² + b² = 3² + 4² = 9 + 16 = 25
c² = 25
25 = 25
c² = a² + b²
This triangle is a right angle triangle.
6, 7, 8
a = 6, b = 7, c = 8
a² + b² = 6² + 7² = 36 + 49 = 85
c² = 8² = 64
64 < 85
c² < a² + b²
This triangle is an acute triangle.
7, 9, 15
a = 7, b = 9, c = 15
a² + b² = 7² + 9² = 49 + 81 = 130
c² = 15² = 225
225 > 130
c² > a² + b²
This triangle is an obtuse triangle.
Hope this Helps!!!