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

Answer:

The inequality (10)< s < (60) represents the possible third side length of the triangle, s, in centimeters.

The inequality (70)< p < (120)represents the possible values for the perimeter, p, of the triangle, in centimeters.

Step-by-step explanation:

Consider the provided information.

The sum of any 2 sides of a triangle must be greater than the measure of the third side.

Let say the third side 's' is the smallest side, then according to above condition.

$25+s>35\\s>35-25\\s>10$

Let say the third side 's' is the largest side, then according to above condition.

$25+35>s\\60>s$

Hence, the combined inequality is: $10$

Perimeter of a triangle is the sum of the length of all sides.

$p=25+35+s\\p=60+s$

If s>10 then the perimeter will be:

$p>60+10$

$p>70$

If 60 then the perimeter will be:

$p$

$p$

Therefore, the combined inequality is: $70$

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

$P < 60+60\\ P$

so

$70\ cm < P < 120\ cm$

therefore

the answer part b) is

$70\ cm < P < 120\ cm$