Question

Given that two sides of a triangle have sides 5 and 7, write the range of the lengths of the third side:

Answer 1

Answer:

Step-by-step explanation:

The two sides add up to 12. If the third "side" of the triangle is 12, then 5 and 7 will lie horizontally on 12.

So the maximum value must be less than 12. What's the smallest x could be?

well 5 + something must be > than 7. If they are not larger than 7, then 5 and something will lie on 7 just as it did before. So how big is something?

5 + y > 7

5 - 5 + y > 7 - 5

y > 2

So the range    is  2 < x < 12

How else could you write this?

2 < x

x < 12 is one way.