Answer:
c must be less than 10 but greater than 4.
Step-by-step explanation:
In order to solve this problem, you have to apply the triangle inequality theorem. This theorem is used to determine whether or not you can form a triangle. According to the theorem, the sum of the two sides must be greater than the longest side of the triangle.
For instance, a triangle has side lengths 4, 5, and 7.
Can you form a triangle with these values?
Well, let's see
Since 4 and 5 are values less than 7, you are going to be adding those numbers. 4 plus 5 is 9. 9 is greater than 7. This means that you can form a triangle with those numbers.
For this question, you are given a triangle that has the side lengths of 3 inches, 7 inches, and c inches. The question wants the range of values. Make c the shortest side and the longest side.
Let's start with longest first.
take 3 and 7
Add them and you will get 10.
10 is greater than c. or c<10.
For the shortest side make 7 the longest
3 plus c is less than 7
subtract 3 from both sides
then you get c is less than 4. or c<4.
So you have c<4 and c>10.
combine them to make a long inequality.
4<c<10.
That is your answer.
