Answer
a) 8, 10, 6
Right angle triangle.
b) 32, 19, 11
Not a triangle
c) 10, 24, 16
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, we will take each of the questions one at a time
a) 8, 10, 6
a = 8
b = 6
c = 10 (longest side)
a² + b² = 8² + 6² = 64 + 36 = 100
c² = 100
100 = 100
c² = a² + b²
Hence, this triangle is a right angle triangle.
b) 32, 19, 11
a = 19
b = 11
c = 32 (longest side)
a + b = 19 + 11 = 30
c = 32
32 > 30
Hence, this triangle is not possible.
c) 10, 24, 16
a = 10
b = 16
c = 24 (longest side)
a² + b² = 10² + 16² = 100 + 256 = 356
c² = 24² = 576
576 > 356
c² > a² + b²
Hence, this triangle is an obtuse triangle.
Hope this Helps!!!