Question

Which of these lengths CANNOT represent the sides of a triangle? {28, 30, 58} {32, 34, 60} {13, 20, 27} {2, 4, 5}

Answer 1

`A.\ {28, 30, 58}`

Explanation:

Required

Which of the lengths do not form a triangle

To do this, we make use of triangle inequality theorem which states that.

`a + b > c`

`b + c > a`

`a + c > b`

Where
`a,\ b\ and\ c` are the sides of the triangle.

So, we have:

`A.\ {28, 30, 58}`

`28 + 30 > 58` --- False

`58 + 30 > 28` --- True

`28 + 58 > 30` --- True

`B.\ {32, 34, 60}`

`32 + 34 > 60` -- True

`32 + 60 > 34` -- True

`34 + 60 > 32` -- True

`C.\ {13, 20, 27}`

`13 + 20 > 27` -- True

`13 + 27 > 20` -- True

`20 + 27 > 13` --- True

`D.\ {2, 4, 5}`

`2 + 4 > 5` --- True

`2 + 5 > 4` -- True

`5 + 4 > 2` --- True

From the computations above, only (A) cannot form a triangle