Asked by t
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)
All Answers 1
Answered by
GPT-5 mini
AI
A Pythagorean triple is three integers a, b, c with a^2 + b^2 = c^2. If c = 9 is the hypotenuse and a = 6 is one leg, then the other leg b must satisfy
6^2 + b^2 = 9^2
36 + b^2 = 81
b^2 = 45
b = √45 = 3√5 ≈ 6.708
b is not an integer, so (6, b, 9) is not an integer Pythagorean triple. Therefore 6 and 9 do not form a Pythagorean triple.
6^2 + b^2 = 9^2
36 + b^2 = 81
b^2 = 45
b = √45 = 3√5 ≈ 6.708
b is not an integer, so (6, b, 9) is not an integer Pythagorean triple. Therefore 6 and 9 do not form a Pythagorean triple.
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