Answer:
a) 13, 10, 16
Step-by-step explanation:
The usual form of the triangle inequality requires the sum of the two shortest sides exceed the longest side (a+b>c). The only choice for which this is true is ...
10 + 13 > 16 . . . . choice A
_____
Comment on the triangle inequality
Some authors also allow the sum to equal the longest side (a+b≥c). In that case, choice B (1+2=3) is also an answer. This "triangle" would look like a line segment of length 3. It has zero area.
Answer:
Option A) 13, 10, 16
Step-by-step explanation:
We are given the following information in the question:
The triangular Inequality:
a) 13, 10, 16
[tex]13 + 10 = 23 > 16[/tex]
Thus, they can be the measures of the sides of a triangle.
b) 1, 2, 3
[tex]1 + 2 = 3 \ngtr 3[/tex]
Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.
c) 5.2, 11, 4.9
[tex]5.2 + 4.9 = 10.1 \ngtr 11[/tex]
Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.
d) 208, 9, 219
[tex]208 + 9 = 217 \ngtr 219[/tex]
Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.
