Question

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

Answer 1

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

Replace the lengths :
Triangle 1 :
`1^(2) + 610^(2) \\eq 810^(2)` (not right triangle, also does not satisfy the triangle inequality, so not a real triangle)
Triangle 2 :
`7^(2) + 7^(2) \\eq 13^(2)` (not right triangle)
Triangle 3 :
`313^(2) + 413^(2) \\eq 513^(2)` (not right triangle)

So, correct answer is D