Question

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

Answer 1

To find the area of the new poster, we first need to determine its dimensions based on the scaling.

The original poster has dimensions:
- Length = 10 ft
- Width = 4 ft

The area of the original poster is:
\[
\text{Area}_{\text{original}} = \text{Length} \times \text{Width} = 10 \, \text{ft} \times 4 \, \text{ft} = 40 \, \text{ft}^2
\]

The new poster has a width of 2 ft. To find the scale factor, we compare the new width to the original width:
\[
\text{Scale factor} = \frac{\text{New Width}}{\text{Original Width}} = \frac{2 \, \text{ft}}{4 \, \text{ft}} = \frac{1}{2}
\]

Now, we apply this scale factor to the length of the original poster:
\[
\text{New Length} = \text{Original Length} \times \text{Scale factor} = 10 \, \text{ft} \times \frac{1}{2} = 5 \, \text{ft}
\]

Now we have the dimensions of the new poster:
- New Length = 5 ft
- New Width = 2 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:
\[
\boxed{10 \, \text{ft}^2}
\]