Question

Please show work. The base of a rectangular box is to be twice as long as it is wide. The volume of the box is 256 cubic inches. The material for the top costs $0.50 per square inch, and the material for the sid

Answer 1

The area of a larger square, whose side lengths are twice that of a smaller square, is four times greater than the area of the smaller square.

Step-by-step explanation:

The student is asking how the area of a larger square compares to the area of a smaller square if the dimensions of the larger square are twice those of the smaller one. To determine this, we use the concept of scale factor in geometry.

If the side length of the smaller square is 4 inches, then the side of the larger square is 4 inches × 2 = 8 inches. To find the area of each square, we square the length of a side. The area of the smaller square is then 4 inches × 4 inches = 16 square inches, and the area of the larger square is 8 inches × 8 inches = 64 square inches.

Therefore, the area of the larger square is 64 square inches / 16 square inches = 4 times greater than the area of the smaller square.