Question

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

Answer 1

A Pythagorean triple is three integers a, b, c with a^2 + b^2 = c^2 (c the hypotenuse). Here a = 6 and c = 9 (so c is the hypotenuse). Compute the other leg b:

b^2 = c^2 − a^2 = 9^2 − 6^2 = 81 − 36 = 45,
b = √45 = 3√5 ≈ 6.708,

which is not an integer. (If 6 and 9 were the two legs, the hypotenuse would be √(36+81)=√117=3√13, also not integer.)

Therefore 6 and 9 do not form a Pythagorean triple.