Question

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

Answer 1

Answer:

Option A) 13, 10, 16

Step-by-step explanation:

We are given the following information in the question:

The triangular Inequality:

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• $\text{Side 1} + \text{Side 2} > \text{Side 3}$

a) 13, 10, 16

$13 + 10 = 23 > 16$

Thus, they can be the measures of the sides of a triangle.

b) 1, 2, 3

$1 + 2 = 3 \ngtr 3$

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

$5.2 + 4.9 = 10.1 \ngtr 11$

Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.

d) 208, 9, 219

$208 + 9 = 217 \ngtr 219$

Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.

Answer 2

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

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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.