Question

Ms. Ford's kitchen is in the shape of a rectangle with a width of 12.25 feet. She is buying a wallpaper border to go on all of her kitchen walls. She wants to buy 5 extra feet of the border to be sure she has enough. She buys 62.5 feet of the border.
What is the length of Ms. Ford's kitchen? Explain how you can find your answer.

Answer 1

To find the length of Ms. Ford's kitchen, we need to first establish the dimensions of the kitchen and how the total amount of wallpaper border relates to those dimensions.

1. **Understanding the Shape and Measurements**:
The kitchen is rectangular with a width of 12.25 feet. We denote the length of the kitchen as \( L \) feet.

2. **Calculating the Perimeter**:
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (L + W)
\]
where \( W \) is the width. In this case, the width \( W \) is 12.25 feet. Thus, the formula becomes:
\[
P = 2 \times (L + 12.25)
\]

3. **Including the Extra Border**:
Ms. Ford bought 62.5 feet of wallpaper border, which includes an additional 5 feet for extra coverage. Therefore, the amount of border actually needed for the perimeter without the extra can be calculated as:
\[
\text{Needed length} = 62.5 \text{ feet} - 5 \text{ feet} = 57.5 \text{ feet}
\]
Therefore, the perimeter of the kitchen (based on the amount of border needed) is 57.5 feet.

4. **Setting up the Equation**:
Setting the formula for perimeter equal to the calculated perimeter, we have:
\[
2 \times (L + 12.25) = 57.5
\]

5. **Solving for Length \( L \)**:
Dividing both sides by 2 to simplify:
\[
L + 12.25 = \frac{57.5}{2} = 28.75
\]
Now, subtract 12.25 from both sides to isolate \( L \):
\[
L = 28.75 - 12.25 = 16.5 \text{ feet}
\]

Thus, the length of Ms. Ford's kitchen is **16.5 feet**.