Select the correct answer.

If rectangle A has a length and width that are *k* times the length and width of rectangle B, which statement is true?

 **A.** 

The perimeter of rectangle A is 2*k* times the perimeter of rectangle B.

 **B.** 

The perimeter of rectangle A is *k*2 times the perimeter of rectangle B.

 **C.** 

The perimeter of rectangle A is *k* times the perimeter of rectangle B.

 **D.** 

The perimeter of rectangle A is *k*3 times the perimeter of rectangle B.

Let's analyze the problem step by step.

Given:
- Rectangle A has a length and width that are \( k \) times the length and width of Rectangle B.

### Perimeter of Rectangle B:
Let the length of Rectangle B be \( l_B \) and the width be \( w_B \).
The perimeter \( P_B \) of Rectangle B is:
\[
P_B = 2(l_B + w_B)
\]

### Perimeter of Rectangle A:
The length and width of Rectangle A will be \( k \times l_B \) and \( k \times w_B \) respectively.
The perimeter \( P_A \) of Rectangle A is:
\[
P_A = 2(k \times l_B + k \times w_B)
\]
\[
P_A = 2k(l_B + w_B)
\]

### Relationship Between Perimeters:
Now, let's express \( P_A \) in terms of \( P_B \):
\[
P_A = 2k(l_B + w_B) = k \times 2(l_B + w_B) = k \times P_B
\]

So, the perimeter of Rectangle A is \( k \) times the perimeter of Rectangle B.

### Correct Answer:
The correct statement is:

**C.** The perimeter of rectangle A is \( k \) times the perimeter of rectangle B.

Would you like more details or have any other questions? 

Here are 5 related questions:
1. What happens to the area of Rectangle A compared to Rectangle B when the length and width are scaled by \( k \)?
2. How does scaling a rectangle's dimensions affect its diagonal length?
3. What if only one dimension of Rectangle A is \( k \) times that of Rectangle B—how does the perimeter change?
4. How would the perimeter change if the width was doubled and the length remained the same?
5. What is the perimeter if the scaling factor \( k \) is a fraction, like \( \frac{1}{2} \)?

**Tip:** Always remember that scaling linear dimensions (like length and width) by a factor scales the perimeter by the same factor, but the area by the square of that factor.

If rectangle A has a length and width that are k times the length and width of rectangle B, which statement is true?

A. The perimeter of rectangle A is 2k times the perimeter of rectangle B.
B. The perimeter of rectangle A is k^2 times the perimeter of rectangle B.
C. The perimeter of rectangle A is k times the perimeter of rectangle B.
D. The perimeter of rectangle A is k^3 times the perimeter of rectangle B.

Discover how scaling the dimensions of a rectangle by a factor k affects its perimeter. This problem involves key concepts in geometry, specifically the relationship between dimension scaling and perimeter changes. Suitable for students in Grades 6-8.

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