Question

What is a possible third side to a triangle with side lengths of 5 and 5

Answer 1

For a triangle, the condition is: the sum of any 2 sides > third side.

I.e. a+b>c, a+c>b, b+c>a.

So, we have:

5+x>5, and 5+5>x.

This means:

5+x>5 => x>0

10>x => x<10.

Answer:

General condition: 0<x<10.

Integer values: x={1,2,3,4,5,6,7,8,9}

Answer 2

The possible third side of the triangle, based on the triangle inequality theorem would be: 0<x<10

The Triangle Inequality Theorem

According to the triangle inequality theorem, three sides will form a triangle if they conform to the following, a + b > c; a + c > b; b + c > a.

Thus, given two sides of a triangle as 5 and 5, let the third side be x.

• Therefore:

5 + 5 > x

10 > x

• Also,

5 + x > 5

x > 5 - 5

x > 0

Therefore, the possible third side of the triangle, based on the triangle inequality theorem would be: 0<x<10

Learn more about the triangle inequality theorem on:

https://brainly.com/question/309896