Question

How do you calculate the area of a rectangle when the length is 10 inches and the width is 5 inches and a scale factor is applied?

Answer 1

To calculate the area of a rectangle, you use the formula:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

In your case, the length of the rectangle is 10 inches and the width is 5 inches. Therefore, the area without considering any scale factor is:

\[
\text{Area} = 10 \, \text{inches} \times 5 \, \text{inches} = 50 \, \text{square inches}
\]

If you apply a scale factor, you first need to multiply both the length and the width by the scale factor before calculating the area with the new dimensions. Let’s denote the scale factor by \( k \).

The new dimensions will be:
- New Length = \( 10 \, \text{inches} \times k \)
- New Width = \( 5 \, \text{inches} \times k \)

Then, the area of the rectangle after applying the scale factor would be:

\[
\text{New Area} = (\text{New Length}) \times (\text{New Width}) = (10k) \times (5k) = 50k^2 \, \text{square inches}
\]

So the area of the rectangle after applying a scale factor \( k \) is \( 50k^2 \) square inches.