Question
cara and beejal would like to reduce a poster into small study card. the original poster has a length of 36 inches and a width of 24 inches, cara and beejal will reduce the poster using a scale factor of 1/6
length of new study card
width of new study card
area of new study card
length of new study card
width of new study card
area of new study card
Answers
GPT-4o mini
To reduce the poster to a study card using a scale factor of \( \frac{1}{6} \), we will multiply the original dimensions by this scale factor.
1. **Length of the new study card**:
\[
\text{New Length} = \text{Original Length} \times \text{Scale Factor}
\]
\[
\text{New Length} = 36 \, \text{inches} \times \frac{1}{6} = 6 \, \text{inches}
\]
2. **Width of the new study card**:
\[
\text{New Width} = \text{Original Width} \times \text{Scale Factor}
\]
\[
\text{New Width} = 24 \, \text{inches} \times \frac{1}{6} = 4 \, \text{inches}
\]
3. **Area of the new study card**:
\[
\text{Area} = \text{New Length} \times \text{New Width}
\]
\[
\text{Area} = 6 \, \text{inches} \times 4 \, \text{inches} = 24 \, \text{square inches}
\]
In summary:
- Length of the new study card: **6 inches**
- Width of the new study card: **4 inches**
- Area of the new study card: **24 square inches**
1. **Length of the new study card**:
\[
\text{New Length} = \text{Original Length} \times \text{Scale Factor}
\]
\[
\text{New Length} = 36 \, \text{inches} \times \frac{1}{6} = 6 \, \text{inches}
\]
2. **Width of the new study card**:
\[
\text{New Width} = \text{Original Width} \times \text{Scale Factor}
\]
\[
\text{New Width} = 24 \, \text{inches} \times \frac{1}{6} = 4 \, \text{inches}
\]
3. **Area of the new study card**:
\[
\text{Area} = \text{New Length} \times \text{New Width}
\]
\[
\text{Area} = 6 \, \text{inches} \times 4 \, \text{inches} = 24 \, \text{square inches}
\]
In summary:
- Length of the new study card: **6 inches**
- Width of the new study card: **4 inches**
- Area of the new study card: **24 square inches**