220k views
19 votes
1

Which one of the following sets of
numbers could represent the lengths of
the sides of a triangle?
A 8
{8, 11, 19}
B {19, 16, 20}
C {3, 4, 8}
D {11, 5, 5

User Thomasmost
by
8.3k points

1 Answer

9 votes

Answer:

B. {16, 19, 20}

Explanation:

The triangle inequality requires for any sides a, b, c you must have ...

a + b > c

b + c > a

c + a > b

The net result of those requirements are ...

  • the sum of the two shortest sides must be greater than the longest side
  • the length of the third side lies between the difference and sum of the other two sides

__

If we look at the offered side length choices, we see ...

A: 8+11 = 19 . . . not > 19; not a triangle

B: 16+19 = 35 > 20; could be a triangle

C: 3+4 = 7 . . . not > 8; not a triangle

D: 5+5 = 10 . . . not > 11; not a triangle

The side lengths {16, 19, 20} could represent the sides of a triangle.

_____

Additional comment

The version of triangle inequality shown above ensures that a triangle will have non-zero area.

The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")

User Ico
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories