The area of the scale model of a garden is 15 square feet. The scale model is enlarged by a scale factor of 3 to create the actual garden. Which expression finds the area of the actual garden?

Question

1.StartFraction 15 over 3 squared EndFraction
2.StartFraction 15 over 3 EndFraction
3.15 times 3
4.15 times 3 squared

Answer 1

To find the area of the actual garden when the scale model is enlarged by a scale factor of 3, you need to square the scale factor since area is two-dimensional.

Given:

• Area of the scale model = 15 square feet
• Scale factor = 3

The area of the actual garden can be found using the following formula:

\[ \text{Area of actual garden} = \text{Area of scale model} \times \text{(scale factor)}^2 \]

Substituting the values we have:

\[ \text{Area of actual garden} = 15 \times 3^2 \]

Calculating \(3^2\):

\[ 3^2 = 9 \]

Then, the area of the actual garden is:

\[ 15 \times 9 \]

So, the correct expression that represents the area of the actual garden is:

4. \(15 \times 3^2\).