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

StartFraction 15 over 3 squared EndFraction
StartFraction 15 over 3 EndFraction
15 times 3
15 times 3 squared

Answer 1

To find the area of the actual garden after enlarging the scale model by a scale factor of 3, we can use the following relationship:

When an area is scaled by a factor \( k \), the new area becomes \( k^2 \) times the original area.

In this case, the scale factor \( k \) is 3. Therefore, the area of the actual garden can be expressed as:

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

Calculating \( 3^2 \) gives us 9, so:

\[ \text{Area of actual garden} = 15 \times 9 \]

Thus, the correct expression to find the area of the actual garden is:

15 times 3 squared.