Chapter 3.1, Problem 39E

a)

To determine

To find: The function that represent the perimeter of the triangle.

Answer to Problem 39E

The function $p\left(h\right)=h+23$ represents the perimeter of the triangle.

Explanation of Solution

Given information: The given figure is given below.

  

Calculation: Let $p\left(h\right)$ be the perimeter of the triangle.

Hence, from the figure,

  $\begin{array}{l}p\left(h\right)=h+23+10\\ \therefore p\left(h\right)=h+23\end{array}$

b)

To determine

To identify: The independent and dependent variable.

Answer to Problem 39E

The independent variable and dependent variable are $h$ and $p$ respectively.

Explanation of Solution

Given information: $p\left(h\right)=h+23$

Calculation: Since the value of $\left(p\right)$ depends on the length of the sides $\left(h\right)$ .

Hence, $\left(h\right)$ is the independent variable and $\left(p\right)$ is dependent variable.

c)

To determine

To find: The domain and range of the function.

Answer to Problem 39E

The domain and range of the function are $\left(3,23\right)$ and $\left(26,46\right)$ .

Explanation of Solution

Given information: The sum of the length of any two sides of a triangle is greater than the length of its third side.

Calculation: Get the domain of the function $p\left(h\right)=h+23$ ,

  $\begin{array}{l}13+10>h\Rightarrow h<23\\ 13+h>10\Rightarrow h>-3\\ 10+h>13\Rightarrow h>3\\ \Rightarrow 3<h<23\end{array}$

Hence, the domain of the function is $\left(3,23\right)$ .

Now, get the range of the function $p\left(h\right)=h+23$

  $\begin{array}{l}\Rightarrow p\left(3\right)=3+23\\ =26\\ \Rightarrow p\left(23\right)=23+23\\ =46\end{array}$

Hence, the range of the function is $\left(26,46\right)$ .