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

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**