Question

3. In the diagram below, what is the relationship between from the number of rectangles and the perimeter of the figure they form?

Answer 1

The perimeter of the rectangle is $\boxed{16}.$

The perimeter of the two rectangle is $\boxed{20}.$

The perimeter of the three rectangle is $\boxed{24}.$

The relationship between the number of rectangle and the perimeter is $\boxed{12 + 4n}.$

Further explanation:

The perimeter the rectangles can be obtained as follows,

$\boxed{{\text{Perimeter}} = 2a + 2b}$

Given:

Explanation:

The perimeter of one rectangle can be obtained as follows,

$\begin{aligned}{\text{Perimeter}} &= 2 \times 6 + 2 \times 2\\&= 12 + 4\\&= 16\\\end{aligned}$

The perimeter of the rectangle is $\boxed{16}.$

The perimeter of one triangle can be obtained as follows,

$\begin{aligned}{\text{Perimeter}}&= 2 \times 6 + 2 \times 2 + 2 \times 2\\&= 12 + 4 + 4\\&= 20\\\end{aligned}$

The perimeter of the two rectangle is $\boxed{20}.$

The perimeter of one triangle can be obtained as follows,

$\begin{aligned}{\text{Perimeter}} &= 2 \times 6 + 2 \times 2 + 2 \times 2 + 2 \times 2\\&= 12 + 4 + 4 + 4\\&= 24\\\end{aligned}$

The perimeter of the three rectangle is $\boxed{24}.$

The relationship between the number of triangles and the perimeter can be expressed as follows,

$\begin{aligned}{\text{Perimeter}}&= 16 + \left( {n - 1} \right) \times 4\\&= 16 + 4n - 4\\&= 12 + 4n\\\end{aligned}$

Here, $n$ represents the number of sides.

The relationship between the number of triangles and the perimeter is $\boxed{12 + 4n}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Rectangle

Keywords: Number, relationship, rectangles, perimeter, number of rectangles, 2 rectangles, 3 rectangles, table, between the sides, represents.

Answer 2

Answer:

The 4th table: (rectangles, perimeter) = (1, 16), (2, 20), (3, 24)

Explanation:

The sums of the numbers shown in each figure are 8, 10, 12. In each case, this sum is half the perimeter of the figure, so the perimeter values are 16, 20, 24.

Only the 4th table shows these values for perimeter.