To answer this question, we can use the Pythagorean Theorem in each case to determine if each of the sides represents a side of a right triangle.
[tex]h^2=a^2+b^2[/tex]This is the algebraic expression of the Pythagorean Theorem. The hypotenuse is the largest side of the triangle.
First case{54, 72, 91}
Hypotenuse = 91
Then, we have:
[tex]91^2=54^2+72^2\Rightarrow8281=2916+5184\Rightarrow8281\ne8100[/tex]They do not represent the sides of a right triangle.
Second case{5, 12, 14)
Hypotenuse = 14
[tex]14^2=5^2+12^2\Rightarrow196=25+144\Rightarrow196\ne169[/tex]They do not represent the sides of a right triangle.
Third case{20, 22, 29}
[tex]29^2=20^2+22^2\Rightarrow841=400+484\Rightarrow841\ne884[/tex]They do not represent the sides of a right triangle.
Fourth case{48, 64, 80}
[tex]80^2=48^2+64^2\Rightarrow6400=2304+4096\Rightarrow6400=6400[/tex]This triple represents the sides of a right triangle.
In summary, the answer is {48, 64, 80} (last option).
