Question

Determine which set of numbers can be the measures of the sides of a triangle.

A. 13, 10, 16
B. 1, 2, 3
C. 5.2, 11, 4.9
D. 208, 9, 219

Answer 1

Answer: The right answer is A. 13, 10, 16

Explanation:

Answer 2

A. 13, 10, 16

Explanation:

If three sides of triangle have measures a, b and c, then

`a+b>c\\ a+c>b\\b+c>a`

Check all options:

A. a=13, b=10, c=16

Thus,

`a+b=13+10=23>16=c\\a+c=13+16=29>10=b\\b+c=10+16=26>13=a`

This option is true

B. a=1, b=2, c=3

Then

`a+b=1+2=3=c,` but
`a+b` must be greater than c, so

this option is false

C. a=5.2, b=11, c=4.9

Then

`a+c=5.2+4.9=10.1<11=b,` but
`a+c` must be greater than b, so

this option is false

D. a=208, b=9, c=219

Then

`a+b=208+9=217<219=c,` but
`a+b` must be greater than c, so

this option is false