Chapter 1.6, Problem 15PPS

a.

To determine

To complete: The function table for the values of length and breadth for the area of rectangle to $36$ square inches.

Answer to Problem 15PPS

The function table for the values of length and breadth for the area of rectangle to be $36$ square inches is mentioned below.

  $\begin{array}{ccc}\text{possible length}\left(inch\right)& \text{possible width}& \text{area of} \text{rectangle}\\ 1& 36& 36\\ 2& 18& 36\\ 3& 12& 36\\ 4& 9& 36\\ 6& 6& 36\\ 9& 4& 36\\ 12& 3& 36\\ 18& 2& 36\\ 36& 1& 36\end{array}$

Explanation of Solution

Given information:

The area of rectangle is $36$ square inches.

Formula:

Area of rectangle is $length*width$ .

Calculation:

Consider the area of rectangle has $36$ square inches.

Recall that area of rectangle is $length*width$ .

Therefore the possible lengths and widths of the rectangle for an area to be $36$ square inches is followed below.

  $\begin{array}{ccc}\text{possible length}\left(inch\right)& \text{possible width}& \text{area of} \text{rectangle}\\ 1& 36& 36\\ 2& 18& 36\\ 3& 12& 36\\ 4& 9& 36\\ 6& 6& 36\\ 9& 4& 36\\ 12& 3& 36\\ 18& 2& 36\\ 36& 1& 36\end{array}$

b.

To determine

To graph: The ordered pairs of the function table mentioned below.

  $\begin{array}{ccc}\text{possible length}\left(inch\right)& \text{possible width}& \text{area of} \text{rectangle}\\ 1& 36& 36\\ 2& 18& 36\\ 3& 12& 36\\ 4& 9& 36\\ 6& 6& 36\\ 9& 4& 36\\ 12& 3& 36\\ 18& 2& 36\\ 36& 1& 36\end{array}$

Answer to Problem 15PPS

The graph mentioned below represents x axis as length and y axis as width.

  

Explanation of Solution

Given information:

The function table is mentioned below.

  $\begin{array}{ccc}\text{possible length}\left(inch\right)& \text{possible width}& \text{area of} \text{rectangle}\\ 1& 36& 36\\ 2& 18& 36\\ 3& 12& 36\\ 4& 9& 36\\ 6& 6& 36\\ 9& 4& 36\\ 12& 3& 36\\ 18& 2& 36\\ 36& 1& 36\end{array}$

Graph:

The graph plotted below represents x axis as length and y axis as width.

  

Interpretation:

Consider the statement to graph the function table as mentioned below.

Recall that the function table is

  $\begin{array}{ccc}\text{possible length}\left(inch\right)& \text{possible width}& \text{area of} \text{rectangle}\\ 1& 36& 36\\ 2& 18& 36\\ 3& 12& 36\\ 4& 9& 36\\ 6& 6& 36\\ 9& 4& 36\\ 12& 3& 36\\ 18& 2& 36\\ 36& 1& 36\end{array}$ .

Here we consider length as x axis and width as y axis.

Therefore the graph we observed above is the graph of function table.