112k views
2 votes
PLEASE HELP - A triangle with side lengths a, b, and c is shown below. Which statement about the side lengths must be true?

PLEASE HELP - A triangle with side lengths a, b, and c is shown below. Which statement-example-1
User PDStat
by
8.0k points

1 Answer

6 votes

Answer:

A

Explanation:

You want to know which inequality must be true regarding the side lengths of a triangle.

Triangle inequality

The triangle inequality requires the sum of any two side lengths be greater than the length of the third side:

a + b > c . . . . . choice A

__

Additional comment

This means it must also be true that ...

a + c > b

b + c > a

Of course, this means the sum of the two shortest sides must be more than the longest side. It also means any side length must lie between the sum and difference of the other two side lengths:

|a - b| < c < a + b

The version of this inequality most often seen uses the > or < symbol. Some authors use the ≥ or ≤ symbol instead. This allows triangles that look like a line segment and have zero area.

User Ad Infinitum
by
7.7k points

No related questions found