Chapter SH, Problem 9.9MPS

(a)

To determine

To calculate: Towrite and graph a function that gives the area of the garden for different widths and length.

Answer to Problem 9.9MPS

The function that gives the area of the garden for different widths and length is $x=1.5y$

Explanation of Solution

Given: T is planning to make a rectangular flower garden. She wants the length of the garden to be $1.5$ times the width

Calculation:

Given that the length of the rectangular garden is $1.5$ times the width

Let the length of rectangular garden be $x$ and width of the rectangular garden be $y$

Thus, function that gives the area of the garden for different widths and length is given as

  $x=1.5y$

For plotting the graph of equation:

When $y=1$

  $\begin{array}{l}x=1.5\left(1\right)\\ x=1.5\end{array}$

When $y=2$

  $\begin{array}{l}x=1.5\left(2\right)\\ x=3.0\end{array}$

When $y=3$

  $\begin{array}{l}x=1.5\left(3\right)\\ x=4.5\end{array}$

When $y=4$

  $\begin{array}{l}x=1.5\left(4\right)\\ x=6.0\end{array}$

Solutions of equation are as follows:

  $\left(1.5,1\right),\left(3.0,2\right),\left(4.5,3\right),\left(6.0,4\right)$

Plotting the points on graph:

Conclusion:

Hence, the function that gives the area of the garden for different widths and length is $x=1.5y$

(b)

To determine

To calculate: To find the area of the garden if the garden is $6$ feet wide

Answer to Problem 9.9MPS

The area of rectangular garden is $54$ square feet.

Explanation of Solution

Given: Width of rectangular garden is $6$ feet and the function that gives the area of the garden for different widths and length is $x=1.5y$

Formula Used:

Area of rectangle is given as

  $Area=Length\times Width$

Calculation:

Given function that gives the area of the garden for different widths and length is

  $x=1.5y$

Also, width of garden is $6$ feet

Length of garden is calculated by substituting $y=6$ in above equation:

  $\begin{array}{l}x=1.5\left(6\right)\\ x=9.0\end{array}$

Now, area of rectangular garden is calculated as

  $Area=Length\times Width$

Thus, area is

  $\begin{array}{l}Area=x\times y\\ Area=9\times 6\\ Area=54\end{array}$

Conclusion:

Hence, the area of rectangular garden is $54$ square feet.