Question

A. write a function that represents the perimeter P of the triangle.

p=___

b. identify the independent and dependent variables.

The independent variable is __ and the independent variable is __.

c. describe the domain and range of the function.

the domain is __ the range is __

Answer 1

Part a)
`P(h)=23+h`

Part b) see the explanation

Part c) The domain for h is
`3\ units < h < 23\ units` and the range is
`26\ units < P < 46\ units`

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

`P(h)=13+10+h`

`P(h)=23+h`

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)
`13+10 > h` --->
`23 > h` --->
`h < 23`

2)
`h+10 > 13` --->
`h > 3`

therefore

The domain for h is the interval (3,23)

`3\ units < h < 23\ units`

Find the range

For h=3 ---->
`P=23+3=26\ units`

For h=23 ---->
`P=23+23=46\ units`

therefore

The range is the interval (26,46)

`26\ units < P < 46\ units`