Question

The scale factor for 2 similiar rectangles is 3. If the area of the smaller rectangle is 8m^2, what is the area of the larger rectangle and how is it written in a mathmatical form to show how you got to the answer.

Answer 1

To determine the area of the larger rectangle, we square the scale factor of 3 to get 9 and multiply it by the area of the smaller rectangle, which is 8 m², resulting in an area of 72 m² for the larger rectangle.

Step-by-step explanation:

To find the area of the larger rectangle, we first need to understand the relationship between the scale factor and the areas of similar figures. Since the scale factor for the two similar rectangles is 3 and the area of the smaller rectangle is 8 m², we use the fact that the area of similar figures is proportional to the square of the scale factor.

The scale factor is 3, so we square this number: 3² = 9. This means that the larger rectangle will have an area that is 9 times that of the smaller rectangle. Therefore, we can calculate the area of the larger rectangle as follows:

Area of larger rectangle = Scale factor squared × Area of smaller rectangle
Area of larger rectangle = 9 × 8 m²
Area of larger rectangle = 72 m²

The area of the larger rectangle is 72 m², exemplifying that the ratio of the areas of similar figures is indeed the square of the scale factor.