Question
The height of a building is in a proportional relationship to the number of its floors. The figure shows the height of a building with 9 floors. Find the constant of proportionality. Then use the constant of proportionality to find the height of a building with 13 floors. Use pencil and paper. What does the constant of proportionality tell you?
The height of a building with
9 floors is 162 feet tall.
Question content area bottom
Part 1
The constant of proportionality is
enter your response here feet per floor.
The height of a building with
9 floors is 162 feet tall.
Question content area bottom
Part 1
The constant of proportionality is
enter your response here feet per floor.
Answers
GPT-4o mini
To find the constant of proportionality, we can use the relationship between the height of the building and the number of floors. The height of a building can be modeled as:
\[
\text{Height} = k \times \text{Number of Floors}
\]
where \( k \) is the constant of proportionality (height per floor).
Given that the height of a building with 9 floors is 162 feet:
\[
162 = k \times 9
\]
To find \( k \), we can rearrange the equation:
\[
k = \frac{162}{9}
\]
Calculating that gives:
\[
k = 18 \text{ feet per floor}
\]
Part 1: The constant of proportionality is \( 18 \) feet per floor.
Now, we can use this constant to find the height of a building with 13 floors:
\[
\text{Height} = k \times \text{Number of Floors} = 18 \times 13
\]
Performing the calculation:
\[
\text{Height} = 234 \text{ feet}
\]
So, the height of a building with 13 floors is \( 234 \) feet.
The constant of proportionality \( k = 18 \) feet per floor tells us that for every additional floor, the height of the building increases by 18 feet. This is a linear relationship, indicating a consistent height increase with each floor added.
\[
\text{Height} = k \times \text{Number of Floors}
\]
where \( k \) is the constant of proportionality (height per floor).
Given that the height of a building with 9 floors is 162 feet:
\[
162 = k \times 9
\]
To find \( k \), we can rearrange the equation:
\[
k = \frac{162}{9}
\]
Calculating that gives:
\[
k = 18 \text{ feet per floor}
\]
Part 1: The constant of proportionality is \( 18 \) feet per floor.
Now, we can use this constant to find the height of a building with 13 floors:
\[
\text{Height} = k \times \text{Number of Floors} = 18 \times 13
\]
Performing the calculation:
\[
\text{Height} = 234 \text{ feet}
\]
So, the height of a building with 13 floors is \( 234 \) feet.
The constant of proportionality \( k = 18 \) feet per floor tells us that for every additional floor, the height of the building increases by 18 feet. This is a linear relationship, indicating a consistent height increase with each floor added.