Answer:
[tex]A.\ {28, 30, 58}[/tex]
Step-by-step explanation:
Required
Which of the lengths do not form a triangle
To do this, we make use of triangle inequality theorem which states that.
[tex]a + b > c[/tex]
[tex]b + c > a[/tex]
[tex]a + c > b[/tex]
Where [tex]a,\ b\ and\ c[/tex] are the sides of the triangle.
So, we have:
[tex]A.\ {28, 30, 58}[/tex]
[tex]28 + 30 > 58[/tex] --- False
[tex]58 + 30 > 28[/tex] --- True
[tex]28 + 58 > 30[/tex] --- True
[tex]B.\ {32, 34, 60}[/tex]
[tex]32 + 34 > 60[/tex] -- True
[tex]32 + 60 > 34[/tex] -- True
[tex]34 + 60 > 32[/tex] -- True
[tex]C.\ {13, 20, 27}[/tex]
[tex]13 + 20 > 27[/tex] -- True
[tex]13 + 27 > 20[/tex] -- True
[tex]20 + 27 > 13[/tex] --- True
[tex]D.\ {2, 4, 5}[/tex]
[tex]2 + 4 > 5[/tex] --- True
[tex]2 + 5 > 4[/tex] -- True
[tex]5 + 4 > 2[/tex] --- True
From the computations above, only (A) cannot form a triangle
