Question

A triangle has side lengths of 3 inches, 7 inches, and c inches. Enter values to write an inequality that describes the possible values for c, the length of the third side of the triangle.

__< C < __

what are the answers to the blanks?

Answer 1

4 < c < 10

Explanation:

I did the question and got it right

Answer 2

`4\ in < c < 10\ in`

Explanation:

we know that

The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

case A)

`c+3 > 7`

`c > 7-3`

`c > 4\ in`

case B)

`3+7 > c`

`10> c`

Rewrite

`c <10\ in`

therefore

`4\ in < c < 10\ in`