Question

In triangle ABC, AB measures 25 cm and AC measures 35 cm. The inequality < s < represents the possible third side length of the triangle, s, in centimeters. The inequality < p < represents the possible values for the perimeter, p, of the triangle, in centimeters.

Answer 1

10 <s< 60

70 <p< 120

did it on edge

Answer 2

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Let

s------> the length of the third side

`25+s > 35 \\ s > 35-25 \\ s> 10\ cm`

`25+35 > s \\ 60 > s \\ s< 60\ cm`

`10\ cm < s < 60\ cm`

therefore

The answer part a) is

`10\ cm < s < 60\ cm`

we know that

the perimeter of a triangle is the sum of the length sides

In this problem

`P=25+35+s\\P=60+s`

For
`s> 10\ cm`

the perimeter is equal to

`P > 60+10\\ P>70\ cm`

For
`s< 60\ cm`

the perimeter is equal to

`P < 60+60\\ P<120\ cm`

so

`70\ cm < P < 120\ cm`

therefore

the answer part b) is

`70\ cm < P < 120\ cm`