Question

Jan makes the array below to show how she wants to arrange some pictures. Which multiplication equation describes Jan’s array?

a. 3 x 4 = 12

b. 4 x 3 = 12

c. 3 x 3 = 9

d. 4 x 4 = 16

Answer 1

The area of the larger square is four times the area of the smaller square because the side length is doubled, making the larger one's side length 8 inches and its area 64 square inches, compared to the smaller square's 16 square inches.

Step-by-step explanation:

The question asked is about how the area of a larger square compares to the area of a smaller square when the side length of the larger square is twice that of the smaller one. To find the dimensions of the larger square, you can use the information provided about the scale factor. If the side length of the smaller square is 4 inches, then the side length of the larger square would be:

4 inches x 2 = 8 inches

Now to compare the area of the two squares, you calculate the area of each:

• Smaller square: 4 inches x 4 inches = 16 square inches
• Larger square: 8 inches x 8 inches = 64 square inches

The area of the larger square is four times the area of the smaller square because the area is a function of the side length squared (A = s²). So if the side length doubles, the area increases by a factor of 2² = 4. Hence, the correct answer is option (b) It will increase by a factor of four.