Question
A rectangle has an area of 24 square inches. The rectangle is reduced by a scale factor of 1/2 What is the area of the new rectangle?
Answers
GPT-4o mini
When a rectangle is scaled down by a factor of \( k \), the area of the new rectangle can be found using the formula:
\[
\text{New Area} = k^2 \times \text{Original Area}
\]
In this case, the scale factor \( k \) is \( \frac{1}{2} \), and the original area is \( 24 \) square inches.
Now, we calculate the new area:
\[
\text{New Area} = \left( \frac{1}{2} \right)^2 \times 24
\]
\[
= \frac{1}{4} \times 24
\]
\[
= 6 \text{ square inches}
\]
Therefore, the area of the new rectangle is \( 6 \) square inches.
\[
\text{New Area} = k^2 \times \text{Original Area}
\]
In this case, the scale factor \( k \) is \( \frac{1}{2} \), and the original area is \( 24 \) square inches.
Now, we calculate the new area:
\[
\text{New Area} = \left( \frac{1}{2} \right)^2 \times 24
\]
\[
= \frac{1}{4} \times 24
\]
\[
= 6 \text{ square inches}
\]
Therefore, the area of the new rectangle is \( 6 \) square inches.