Answer: The possible length of the third side is 10 inches.
Step-by-step explanation: One of the rules for calculating the side of a triangle in mathematics is the Pythagoras theorem. However, for the Pythagoras theorem to be applied, the triangle must be a right angled triangle. In the question above, we have two sides in a triangle given as 6 inches and 8 inches.
The Pythagoras theorem states that, in any right angled triangle, the square of the hypotenuse (longest side) must be equal to the sum of the squares of the other two sides. Hence, AC^2 = BC^2 + AB^2
Where AC is the hypotenuse and BC and AB are the other two sides. We now have,
AC^2 = 8^2 + 6^2
AC^2 = 64 + 36
AC^2 = 100
Add the square root sign to both sides of the equation
AC = 10.
Therefore the length of the third side measures 10 inches. (This is only possible if the triangle is a right angled triangle)
