Question

Consider a right-angled triangle with sides a=6
and c=9
. Determine whether these values form a Pythagorean triple. Show your steps and explain your answer. (2 points)

Answer 1

To determine if the values form a Pythagorean triple, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is given by:
a^2 + b^2 = c^2

Given that a=6 and c=9, we can substitute these values into the equation:
6^2 + b^2 = 9^2
36 + b^2 = 81

Subtracting 36 from both sides:
b^2 = 81 - 36
b^2 = 45

Taking the square root of both sides to solve for b:
b = √45
b = 3√5

Therefore, the values a=6, b=3√5, and c=9 do not form a Pythagorean triple because they do not satisfy the Pythagorean theorem a^2 + b^2 = c^2.