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:
-
If \( L_B = 4.5 \) inches: \[ W_B = 4.5 - 4.5 = 0 \text{ inches (not valid)} \]
-
If \( L_B = 3 \) inches: \[ W_B = 4.5 - 3 = 1.5 \text{ inches (valid)} \]
-
If \( L_B = 6 \) inches: \[ W_B = 4.5 - 6 = -1.5 \text{ inches (not valid)} \]
-
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.