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The side lengths of three triangles are shown in the table. Which of the triangles is a right triangle? Select all that apply. Triangle Side Lengths | 610 810 1 || 7 7 13 ||| 313 413 513 A. Triangle I B. Triangle II C. Triangle III D. None of the above E. All of the above

Sagot :

Aisinidn

To identify whether or not a triangle is a right triangle, it must satisfy the pythagorean theorem :  [tex]a^{2}+ b^{2} =c^{2}[/tex] (where a;b;c represent the 3 sides, and c being the hypotenuse)

Replace the lengths :
Triangle 1 : [tex]1^{2} + 610^{2} \neq 810^{2}[/tex] (not right triangle, also does not satisfy the triangle inequality, so not a real triangle)
Triangle 2 : [tex]7^{2} + 7^{2} \neq 13^{2}[/tex] (not right triangle)
Triangle 3 : [tex]313^{2} + 413^{2} \neq 513^{2}[/tex] (not right triangle)

So, correct answer is D

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