Question

Which of the following sets of numbers could not represent the three sides of a right triangle?
Answer
Multiple Choice Answers
left curly bracket, 51, comma, 69, comma, 85, right curly bracket{51,69,85}
left curly bracket, 18, comma, 24, comma, 30, right curly bracket{18,24,30}
left curly bracket, 12, comma, 35, comma, 37, right curly bracket{12,35,37}
left curly bracket, 25, comma, 60, comma, 65, right curly bracket{25,60,65}

Answer 1

{51, 69, 85}

Reason: For a right triangle the squares of the two legs must sum to the square of the hypotenuse.
- 18^2 + 24^2 = 30^2 (324 + 576 = 900)
- 12^2 + 35^2 = 37^2 (144 + 1225 = 1369)
- 25^2 + 60^2 = 65^2 (625 + 3600 = 4225)
But 51^2 + 69^2 = 2601 + 4761 = 7362 ≠ 85^2 = 7225, so {51,69,85} cannot be the sides of a right triangle.