Question

An art store sells packages of two different sized square picture frames. The side length of the larger frame, S(x) is modeled by the function S(x) = 3sqrt(x - 1) where is the area of the smaller frame in square inches Which graph shows S(x) ?

Answer 1

The area of the larger square is four times larger than the area of the smaller square since its dimensions are twice as large, and the area scales by the square of the factor.

Step-by-step explanation:

The question asks how the area of a larger square compares to the area of a smaller square, given that the side length of the larger square is twice that of the smaller one. If Marta has a square with a side length of 4 inches, and she creates a similar square with dimensions that are twice the size, the side length of the larger square would be 4 inches × 2 = 8 inches.

To determine how the areas compare, we square the side lengths of both squares. The area of the smaller square is 4 inches × 4 inches = 16 square inches. The area of the larger square is 8 inches × 8 inches = 64 square inches. Therefore, the area of the larger square is 64/16 = 4 times larger than the area of the smaller square. This demonstrates the concept that when the dimensions of a similar geometric shape are scaled up by a factor, the area is scaled up by the square of that factor.