Question

 

Constructed Response 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 and while writting if a 5th grade wroite this

​

Answer 1

To find the length of Ms. Ford's kitchen, we need to use the information given about the wallpaper border she bought. We know that the kitchen is in the shape of a rectangle, and we have the width and the total amount of wallpaper border she purchased.

First, let's understand the perimeter of a rectangle. The formula for the perimeter \( P \) of a rectangle is:

\[
P = 2 \times \text{length} + 2 \times \text{width}
\]

We know the width of Ms. Ford's kitchen is 12.25 feet. We also know that she bought 62.5 feet of wallpaper border, and she bought 5 extra feet to make sure she has enough. So, to find out how much border she actually needed to cover all the walls, we can subtract the 5 extra feet from the total she bought:

\[
62.5 \text{ feet} - 5 \text{ feet} = 57.5 \text{ feet}
\]

Now, we can use this amount to find the perimeter of the kitchen. So we have:

\[
P = 57.5 \text{ feet}
\]

Plugging this value into the perimeter formula, we get:

\[
57.5 = 2 \times \text{length} + 2 \times 12.25
\]

Next, we can simplify the equation. First, calculate \( 2 \times 12.25 \):

\[
2 \times 12.25 = 24.5
\]

Now, substitute this back into the equation:

\[
57.5 = 2 \times \text{length} + 24.5
\]

To isolate \( 2 \times \text{length} \), we can subtract 24.5 from both sides:

\[
57.5 - 24.5 = 2 \times \text{length}
\]

This simplifies to:

\[
33 = 2 \times \text{length}
\]

Now, to find the length, we divide both sides by 2:

\[
\text{length} = \frac{33}{2} = 16.5 \text{ feet}
\]

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

To summarize, I found the length by first determining how much border she actually needed after taking away the extra 5 feet. Then I used the perimeter formula for a rectangle, plugged in the values, and solved for the length.