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

Answer:

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

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.

$a + b > c$

$b + c > a$

$a + c > b$

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