Chapter 4.5, Problem 3P

(a)

To determine

To Evaluate: A function rule for the area of a triangle. Find area of the triangle when length is 16 in.

Answer to Problem 3P

  $A=b^2+2b$

Area of the triangle is 288 square inches

Explanation of Solution

Given information: The height of the triangle is 4 inch more than twice the base of the triangle.

Length of the base is 16 in.

Identify the function rule: The function rule to find the area of the triangle.

Let ‘b’ be the base of the triangle

Height of the triangle is 4 inch more than twice the base of the triangle

  $h=2b+4$

Area of the triangle ‘A’ is

  $\begin{array}{l}Area=\frac{base·height}{2}\\ height=2b+4\\ Area=\frac{b·(2b+4)}{2}=\frac{2b^2+4b}{2}=b^2+2b\\ A=b^2+2b\end{array}$

Evaluate:

  $A=b^2+2b$

Base of the triangle is 16 in. Substitute 16 for ‘b’

  $\begin{array}{l}A=b^2+2b\\ A={16}^2+2(16)=288\end{array}$

Area of the triangle is 288 square inches

(b)

To determine

To graph: Graph the function that is used to find the area of the triangle.

Answer to Problem 3P

  

Function rule is not linear

Explanation of Solution

Given information: Function rule to find area of the triangle

  $A=b^2+2b$

Graph: Graph the function rule using the table. Assume some numbers for b and find the area

Base(b)	Area(A)
0	0
4	24
5	35

Plot the coordinate on the graph

  

The graph is a curve. The graph is not a straight line. So , it is not linear

The rule is non linear.