Chapter 5.6, Problem 16IP

To determine

To find: The missing values in the given table for a proportional relationship.

Answer to Problem 16IP

The complete table is given below:

Side Length $\left(\text{ft}\right)$	$2$	$4$	$7$	$9$
Perimeter of Regular Pentagon $\left(\text{ft}\right)$	$10$	$20$	$35$	$45$

Explanation of Solution

Given information:The table is given as:

Side Length $\left(\text{ft}\right)$	$?$	$4$	$7$	$9$
Perimeter of Regular Pentagon $\left(\text{ft}\right)$	$10$	$20$	$?$	$?$

Calculation:

As given the perimeter of regular pentagon is proportional to the side length, this means the constant of proportionality is constant for each value.

As given the perimeter of regular pentagon is $20\text{ft}$ for $4\text{ft}$ side length. So, the constant of proportionality is:

  $\frac{20}{4}=5$

This means that the perimeter of regular pentagon increases by $5\text{ft}$ for each feet increase in side length. So, the perimeter for regular pentagonof $n\text{ft}$ side length is:

  $P=5n\text{ft}$

Substitute $7$ for $n$ in the formula for perimeter.

  $\begin{array}{c}P=5\times 7\text{ft}\\ =35\text{ft}\end{array}$

So, the perimeter of regular pentagon of side length $7\text{ft}$ is $35\text{ft}$ .

Substitute $9$ for $n$ in the formula for perimeter.

  $\begin{array}{c}P=5\times 9\text{ft}\\ =45\text{ft}\end{array}$

So, the perimeter of regular pentagon of side length $9\text{ft}$ is $45\text{ft}$ .

Substitute $10\text{ft}$ for $P$ in the formula for perimeter.

  $\begin{array}{c}10\text{ft}=5n\text{ft}\\ n=\frac{10\text{ft}}{5\text{ft}}\\ n=2\end{array}$

So, the side length for $10\text{ft}$ perimeter is $2$ .

Therefore, the complete table is shown below:

Side Length $\left(\text{ft}\right)$	$2$	$4$	$7$	$9$
Perimeter of Regular Pentagon $\left(\text{ft}\right)$	$10$	$20$	$35$	$45$