ia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants.

Question

ia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants.

Answer the following questions using this information. Be sure to work out your problems on paper and use a calculator if needed.

1a. Mia will use one of these boards for the length of the shelter. She knows she wants the length of the shelter to measure 3.25 feet. She will use a different board for the width of the shelter. The width of the shelter will be shorter than the length.

Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches?

(2 points)
Responses

Board 1 that measures 36 inches
Board 1 that measures 36 inches

Board 2 that measures 39 inches
Board 2 that measures 39 inches

Board 3 that measures 42
Board 3 that measures 42
Question 2

1b. Use the information from question 1a to solve this question.

What is the width of the shelter, measured in FEET? *Remember the width will be shorter than the length.

(2 points)
Responses

3 feet
3 feet

3.25 feet
3.25 feet

3.5 feet
3.5 feet
Question 3

1c. Mia needs to cut the third board to match the width of the shelter. How many feet of board will she need to cut off the existing board to reach this goal?

(2 points)
Responses

6 inches or 0.5 feet
6 inches or 0.5 feet

3 inches or 0.25 feet
3 inches or 0.25 feet

12 inches or 1 foot
12 inches or 1 foot
Question 4

1d. For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. Which of these, if any, will cover all the space needed for the roof?

1 foot = 1/3 of a yard

(2 points)
Responses

The board measuring 1 square yard
The board measuring 1 square yard

The board measuring 3 feet by 3 feet
The board measuring 3 feet by 3 feet

The board measuring 36 inches by 36 inches
The board measuring 36 inches by 36 inches

None of these boards will work

Answer 1

Bot GPT 4-o mini answered
4 hours ago

Let's work through each question step by step based on the information you provided.

Question 1a

Mia wants the length of the shelter to measure 3.25 feet. First, let's convert 3.25 feet into inches:

\[ 3.25 \text{ feet} = 3.25 \times 12 \text{ inches} = 39 \text{ inches} \]

Now we check which board is suitable for the length of 39 inches. The available boards are:

Board 1: 36 inches
Board 2: 39 inches
Board 3: 42 inches

Mia will use Board 2 that measures 39 inches for the length of the shelter.

Question 1b

The width of the shelter must be shorter than the length. Since she is using 39 inches (3.25 feet) for the length, she can use either of the remaining boards (36 inches or 42 inches). However, both the 36-inch board is shorter than the length option:

\[ 36 \text{ inches} = 3 \text{ feet} \]

Thus, the width of the shelter should be 3 feet.

Question 1c

Mia needs to cut the third board (which measures 42 inches) to match the width of the shelter (36 inches). To find out how much she needs to cut off:

\[ 42 \text{ inches} - 36 \text{ inches} = 6 \text{ inches} \]

Convert 6 inches to feet:

\[ 6 \text{ inches} = 0.5 \text{ feet} \]

So, Mia will need to cut off 6 inches or 0.5 feet.

Question 1d

For the roof, Mia has three options:

1 square yard: Convert this to square feet (since 1 yard = 3 feet):

\[ 1 \text{ square yard} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]
3 feet by 3 feet: Calculate the area:

\[ 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]
36 inches by 36 inches: Convert to feet (since 36 inches = 3 feet):

\[ 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]

Each of the boards covers 9 square feet. Therefore, all of these boards (the board measuring 1 square yard, the board measuring 3 feet by 3 feet, and the board measuring 36 inches by 36 inches) will cover all the space needed for the roof.

Summary of Answers:

Board 2 that measures 39 inches (for the length).
3 feet (for the width).
6 inches or 0.5 feet (to cut off the board).
The board measuring 1 square yard, The board measuring 3 feet by 3 feet, and The board measuring 36 inches by 36 inches will all work.