Question

Rectangle A has a perimeter of 27 inches and Rectangle B has a perimeter of 9 inches. If the length of Rectangle A is 9 inches, which of the following could represent the length of Rectangle B?(1 point)
Responses

4.5 inches
4.5 inches

3 inches
3 inches

6 inches
6 inches

10 inches

Answer 1

To find the possible length for Rectangle B, we first need to calculate the dimensions of Rectangle A and then use the perimeter formula for Rectangle B.

The perimeter \( P \) of a rectangle is given by:

\[
P = 2(L + W)
\]

Where \( L \) is the length and \( W \) is the width.

For Rectangle A, we know the perimeter is 27 inches and the length is 9 inches. We can find the width:

\[
27 = 2(9 + W)
\]

Dividing both sides by 2:

\[
13.5 = 9 + W
\]

Subtracting 9 from both sides:

\[
W = 13.5 - 9 = 4.5 \text{ inches}
\]

Now we have the dimensions of Rectangle A: length = 9 inches and width = 4.5 inches.

Now let’s analyze Rectangle B, which has a perimeter of 9 inches. If we denote the length of Rectangle B as \( L_B \) and its width as \( W_B \), we can set up the perimeter equation:

\[
9 = 2(L_B + W_B)
\]

Dividing both sides by 2:

\[
4.5 = L_B + W_B
\]

Now we need to find the possible length \( L_B \) given the responses. Let’s evaluate each option:

1. **If \( L_B = 4.5 \) inches**:
\[
W_B = 4.5 - 4.5 = 0 \text{ inches (not valid)}
\]

2. **If \( L_B = 3 \) inches**:
\[
W_B = 4.5 - 3 = 1.5 \text{ inches (valid)}
\]

3. **If \( L_B = 6 \) inches**:
\[
W_B = 4.5 - 6 = -1.5 \text{ inches (not valid)}
\]

4. **If \( L_B = 10 \) inches**:
\[
W_B = 4.5 - 10 = -5.5 \text{ inches (not valid)}
\]

The only valid length for Rectangle B is:

**3 inches**

So the correct response is **3 inches**.