Question

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. a 11.5 and 23.6

Answer 1

`12.1 < Y < 35.1`

Explanation:

Given

Sides: 11.5 and 23.6

Required

Determine the range of the third side

Let the third side with Y

Two of the following conditions must be satisfied to calculate the range of the third side

`11.5 + Y > 23.6`

`23.6+ Y > 11.5`

`11.5 + 23.6 > Y`

We'll solve one after other

1.
`11.5 + Y > 23.6`

`Y > 23.6 - 11.5`

`Y > 12.1`

2.
`23.6+ Y > 11.5`

`Y > 11.5- 23.6`

`Y > -12.1`

3.
`11.5 + 23.6 > Y`

`35.1 > Y`

`Y < 35.1`

Inequalities with negative can't be used' So, we have

`Y > 12.1` and
`Y < 35.1`

Rewrite inequality

`12.1 < Y` and
`Y < 35.1`

Combine inequality

`12.1 < Y < 35.1`