Q8. - Algebra 1

Question

The edge of each box below is 1 unit long.

a. Make a table showing the perimeters of the first 3 figures in the pattern.

b. Look for a pattern in the perimeters of the shapes. Write an algebraic expression for the perimeter of Figure n.

c. What would be the perimeter of Figure 10 in the pattern?

Step-by-Step Solution

Answer

a. The table showing the perimeters of the first 3 figures in the pattern is as follows:

Figure	Perimeter
1	4
2	12
3	20

 

b. The algebraic expression of figure n is $8n-4$.

c. The perimeter of Figure 10 in the pattern is 76 units.

Part a. Step 1. Given information.

The figure given in the question for which we have to find the perimeter is as follows:

Part a. Step 2. Concept.

For the perimeter, we have to count the edges of the given figures.

Part a. Step 3. To find the perimeter of the given figures.

In the first figures, the total number of edges are 4.

In the second figure, the total number of edges are 12.

In the third figure, the total number of edges are 20.

Therefore,

The table showing the perimeters of the first 3 figures in the pattern is as follows:

Figure	Perimeter
1	4
2	12
3	20

 

Part b. Step 1. Given information.

The figure given in the question for which we have to find the perimeter is as follows:

Part b. Step 2. Concept.

From the given figures, we can see that,

In each figure, the perimeter of each figure is increasing by 8 units each time.

Part b. Step 3. To find the algebraic expression for Figure n.

As the perimeters are increasing by 8 each time. Therefore, the algebraic expression is $8n-4$.

Therefore,

The algebraic expression of figure n is $8n-4$.

Part c. Step 1. Given information.

The figure given in the question for which we have to find the perimeter is as follows:

Part c. Step 2. Concept.

For finding the perimeter of figure 10 in the pattern, we have to put $n=10$ in the algebraic expression which we find in the previous part.

Part c. Step 3. To find the perimeter of Figure 10 in the pattern.

Substitute $n=10$ in the expression $8n-4$.

$$\begin{gathered} P=8\left(10\right)-4 \\ =80-4 \\ =76 \end{gathered}$$

 

Therefore, the perimeter is 76 units.