Question

You have two rectangles. Each has sides of length 4 and 9. You place them together side by side to form a larger rectangle.

It can have length ​4, width 9+9​, and area 4*9+4*9.
It can have length 9​, width 4+4​, and area 9*4+9*4.
It can have length 4​, width 9+4​, and area 4*9+4*4.
Its area must be 72.

Answer 1

The area of the larger square is four times larger than the area of the smaller square because the side lengths are twice as long, and the area scales with the square of the scale factor.

Step-by-step explanation:

When comparing the area of two similar geometric shapes, such as squares, we find that the area of the larger figure is the square of the scale factor times the area of the smaller figure. In this case, Marta has an original square with side length of 4 inches, and a similar square with side lengths twice that of the original. This gives us a scale factor of 2. Since the area is proportional to the square of the side lengths, the area of the larger square is 4 times larger than the area of the smaller square.

The original square has an area of 4 inches x 4 inches which is 16 square inches. The larger square has side lengths of 8 inches (4 inches x 2) and therefore an area of 8 inches x 8 inches, which is 64 square inches. So, the area of the larger square is indeed 4 times larger than that of the smaller square.