Question
A poster has length of 10 and width of 4 ft. New poster is redone to scale and has a width of 2ft. What is area of new poster? Must include proper units
Answers
GPT-4o mini
To find the area of the new poster, we first need to determine the scale factor used to resize the poster.
The original poster has:
- Length = 10 ft
- Width = 4 ft
The area of the original poster can be calculated as follows:
\[
\text{Area}_{\text{original}} = \text{Length} \times \text{Width} = 10 \, \text{ft} \times 4 \, \text{ft} = 40 \, \text{ft}^2
\]
The new poster has a width of 2 ft. To find the scale factor, we compare the width of the new poster to the original:
\[
\text{Scale factor} = \frac{\text{Width of new poster}}{\text{Width of original poster}} = \frac{2 \, \text{ft}}{4 \, \text{ft}} = \frac{1}{2}
\]
Since the poster is scaled down by a factor of \( \frac{1}{2} \), the new length will also be scaled down by the same factor:
\[
\text{New Length} = \text{Original Length} \times \text{Scale factor} = 10 \, \text{ft} \times \frac{1}{2} = 5 \, \text{ft}
\]
Now, we can calculate the area of the new poster:
\[
\text{Area}_{\text{new}} = \text{New Length} \times \text{New Width} = 5 \, \text{ft} \times 2 \, \text{ft} = 10 \, \text{ft}^2
\]
Thus, the area of the new poster is \( \boxed{10 \, \text{ft}^2} \).
The original poster has:
- Length = 10 ft
- Width = 4 ft
The area of the original poster can be calculated as follows:
\[
\text{Area}_{\text{original}} = \text{Length} \times \text{Width} = 10 \, \text{ft} \times 4 \, \text{ft} = 40 \, \text{ft}^2
\]
The new poster has a width of 2 ft. To find the scale factor, we compare the width of the new poster to the original:
\[
\text{Scale factor} = \frac{\text{Width of new poster}}{\text{Width of original poster}} = \frac{2 \, \text{ft}}{4 \, \text{ft}} = \frac{1}{2}
\]
Since the poster is scaled down by a factor of \( \frac{1}{2} \), the new length will also be scaled down by the same factor:
\[
\text{New Length} = \text{Original Length} \times \text{Scale factor} = 10 \, \text{ft} \times \frac{1}{2} = 5 \, \text{ft}
\]
Now, we can calculate the area of the new poster:
\[
\text{Area}_{\text{new}} = \text{New Length} \times \text{New Width} = 5 \, \text{ft} \times 2 \, \text{ft} = 10 \, \text{ft}^2
\]
Thus, the area of the new poster is \( \boxed{10 \, \text{ft}^2} \).