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
.(3 points)
Determine the dimensions and area of the study card.

7th Grade Math Formula Sheet

Length of the new study card =
inches

Width of the new study card =
inches

Area of the new study card =
square inches

Answer 1

To reduce the dimensions of the original poster using a scale factor of \( \frac{1}{6} \), we can apply the scale factor to both the length and the width of the poster.

### Step 1: Calculate the dimensions of the study card

1. **Length of the new study card**:
\[
\text{Length} = \text{Original Length} \times \text{Scale Factor}
\]
\[
\text{Length} = 36 \text{ inches} \times \frac{1}{6} = 6 \text{ inches}
\]

2. **Width of the new study card**:
\[
\text{Width} = \text{Original Width} \times \text{Scale Factor}
\]
\[
\text{Width} = 24 \text{ inches} \times \frac{1}{6} = 4 \text{ inches}
\]

### Step 2: Calculate the area of the study card

The area of a rectangle is calculated as:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
\[
\text{Area} = 6 \text{ inches} \times 4 \text{ inches} = 24 \text{ square inches}
\]

### Final Results:
- **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

These are the dimensions and area of the study card.