Answer:
Part a) [tex]P(h)=23+h[/tex]
Part b) see the explanation
Part c) The domain for h is [tex]3\ units < h < 23\ units[/tex] and the range is [tex]26\ units < P < 46\ units[/tex]
Step-by-step explanation:
Let
h ----> the measure of the third side of triangle
P ---> the perimeter of triangle
Part a) write a function that represents the perimeter P of the triangle
we know that
The perimeter of triangle is equal to the sum of its three length sides
so
[tex]P(h)=13+10+h[/tex]
[tex]P(h)=23+h[/tex]
Part b) Identify the independent and dependent variables
In this problem
The independent variable or input value is the measure of the third side of triangle h
The dependent variable or output value is the perimeter of triangle P
Part c) Describe the domain and range of the function
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
Find the possible measures of h
Applying the Triangle Inequality Theorem
1) [tex]13+10 > h[/tex] ---> [tex]23 > h[/tex] ---> [tex]h < 23[/tex]
2) [tex]h+10 > 13[/tex] --->[tex]h > 3[/tex]
therefore
The domain for h is the interval (3,23)
[tex]3\ units < h < 23\ units[/tex]
Find the range
For h=3 ----> [tex]P=23+3=26\ units[/tex]
For h=23 ----> [tex]P=23+23=46\ units[/tex]
therefore
The range is the interval (26,46)
[tex]26\ units < P < 46\ units[/tex]
