Based on the side lengths given (a, b, and c), the triangle that is a right triangle is a = 6, b = 8, c = 10 (option 2)
Pythagoras theory
Let a, b and c (the longest) be the sides of a triangle. Then the sum of the squares of a and b must be equal to the square of c as shown below
a² + b² = c²
With the above formula in mind, we shall determine the triangle that is right triangle.
Option 1
a = 4
b = 6
c = 8
a² + b² = c²
4² + 6² = 8²
16 + 36 = 64
52 ≠ 64
Option 2
a = 6
b = 8
c = 10
a² + b² = c²
6² + 8² = 10²
36 + 64 = 100
100 = 100
Option 3
a = 5
b = 6
c = 161
a² + b² = c²
5² + 6² = 161²
25 + 36 = 25921
61 ≠ 25921
Option 4
a = 6
b = 9
c = 12
a² + b² = c²
6² + 9² = 12²
36 + 81 = 144
117 ≠ 144
From the above illustration, only option 2 (a = 6, b = 8, c = 10) agrees with the pythagoras theory.
Therefore, a = 6, b = 8, c = 10 (option 2) is a right triangle
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