Chapter 8.2, Problem 9CYU

To determine

To calculate: To find which figure will have a perimeter of $60$ feet

Answer to Problem 9CYU

Figure 15 has perimeter of $60$ feet.

Explanation of Solution

Given information: Each side of a square has a length of $1$ foot. Sequence of figures is

  

Formula Used:

Term: In a sequence, each number is referred to as a term

Term Number: In a sequence, the position of the given term is referred to as term number.

When the difference between the consecutive terms of a sequence is common, then the sequence is an arithmetic sequence.

Calculation:

Given the sequence of figures as follows:

  

From above figure,

Perimeter of Figure 1 $=4$

Perimeter of Figure 2 $=8$

Perimeter of Figure 3 $=12$

Sequence is given as follow:

  $4,8,12,\mathrm{...}$

Here, the first term of the sequence is $a=4$

Also, the common difference is

  $d=8-4=12-8=4$

Since the difference is common, hence the sequence in arithmetic sequence.

Let term is denoted by $t$ and term number is denoted as $n$

Thus, nth term of arithmetic sequence is given as

  $t=a+\left(n-1\right)d$

Also, we need to find the figure that has perimeter of $60$

Thus,

  $t=60$

Substituting the values in above equation,

  $\begin{array}{l}60=4+\left(n-1\right)4\\ 60=4+4n-4\\ 60=4n\\ n=\frac{60}{4}\\ n=15\end{array}$

Hence, figure 15 has perimeter of $60$ feet