Chapter 8.3, Problem 35PPS

(a)

To determine

To calculate: To write the equation for the situation.

Answer to Problem 35PPS

Equation is $x+y=8$

Explanation of Solution

Given information: A rectangle is $x$ inches long and $y$ inches wide and has a perimeter of $16$ inches

  

Formula Used:

Perimeter of rectangle is given as

  $Perimeter=2\left(Length+Width\right)$

Calculation:

Given that a rectangle is $x$ inches long and $y$ inches wide and has a perimeter of $16$ inches

Perimeter of rectangle is given as

  $\begin{array}{l}Perimeter=2\left(Length+Width\right)\\ 16=2\left(x+y\right)\\ x+y=8\end{array}$

Conclusion:

Hence, equation is $x+y=8$

(b)

To determine

To calculate: To write three ordered pairs (width, length) that satisfy the equation

Answer to Problem 35PPS

Three ordered pairs (width, length) are $\left(2,6\right),\left(4,4\right),\left(6,2\right)$

Explanation of Solution

Given information: A rectangle is $x$ inches long and $y$ inches wide and has a perimeter of $16$ inches

  

Calculation:

Equation is given as

  $x+y=8$

When $x=6$

  $\begin{array}{l}y=8-6\\ y=2\end{array}$

When $x=4$

  $\begin{array}{l}y=8-4\\ y=4\end{array}$

When $x=2$

  $\begin{array}{l}y=8-2\\ y=6\end{array}$

Hence, ordered pairs (width, length) are

  $\left(2,6\right),\left(4,4\right),\left(6,2\right)$

Conclusion:

Hence, ordered pairs are $\left(2,6\right),\left(4,4\right),\left(6,2\right)$

(c)

To determine

To calculate: To graph the ordered pairs and then draw a line through the points

Answer to Problem 35PPS

Ordered pairs are plotted.

Explanation of Solution

Given information: A rectangle is $x$ inches long and $y$ inches wide and has a perimeter of $16$ inches

  

Calculation:

Equation is given as

  $x+y=8$

The ordered pairs are $\left(2,6\right),\left(4,4\right),\left(6,2\right)$

Plotting the point on graph:

  

Conclusion:

Hence, ordered pairs are plotted

(d)

To determine

To calculate: To find if the ordered pair $\left(-4,12\right)$ is solution of equation and to find if it makes sense in the context of the situation.

Answer to Problem 35PPS

Ordered pairs are plotted.

Explanation of Solution

Given information: A rectangle is $x$ inches long and $y$ inches wide and has a perimeter of $16$ inches

  

Calculation:

Equation is given as

  $x+y=8$

To find if ordered pair $\left(-4,12\right)$ is solution of above equation or not, substitute the values in equation

Left hand side of equation is calculated as

  $\begin{array}{l}\Rightarrow -4+12\\ \Rightarrow 8\end{array}$

Left hand side of equation is equal to right hand side

Thus, $\left(-4,12\right)$ is the solution of equation.

Also, it does make sense in the context of the situation as the width of rectangle can never be a negative value

Conclusion:

Hence, $\left(-4,12\right)$ is the solution of equation.