Question

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

Answer 1

Answer:

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 $26\ units < P < 46\ units$

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

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

$P(h)=23+h$

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)

$26\ units < P < 46\ units$