Chapter 4.2, Problem 1P

(a)

To determine

To find the relationship between the number of triangles and the perimeter of the figure they form.

Explanation of Solution

Given:

The given diagrams are-

Calculation:

The following table shows the number of triangles and the perimeter-

Number of Triangles	Perimeter
1	10
2	14
3	18
4	22

(b)

To determine

To find out how will you determine the perimeter of $n+1$ triangles if you know the perimeter of $n$ triangles?

Answer to Problem 1P

The perimeter of $n+1$ triangles will be $4$ more than the the perimeter of $n$ triangles.

Explanation of Solution

On the basis of the table obtained in part (a), it is clear that the perimeter of $n+1$ triangles will be $4$ more than the the perimeter of $n$ triangles.

(c)

To determine

To find out how the answer in part (a) is related to part (b).

Answer to Problem 1P

The perimeter of $n+1$ triangles will be $4$ more than the the perimeter of $n$ triangles.

Explanation of Solution

On the basis of the table obtained in part (a), it is clear that the perimeter of $n+1$ triangles will be $4$ more than the the perimeter of $n$ triangles.