A rectangular box has a length of 3 inches, a width of 2 inches, and a height of 4 inches. Find the dimensions of the three similar boxes: one that has a length of 6 inches, one that has a width of 6 inches, and one that has a heght of 6 inches.

Step-by-step explanation:

When two plane figures are similar in size, it means that there is a constant ratio between the size of the corresponding sides.

A rectangular box has a length of 3 inches, a width of 2 inches, and a height of 4 inches.

1) if a similar box has a length of 6 inches, it means that the ratio of its length to that of the original rectangle would be

6/3 = 2

The width of the new rectangle would be 2 * 2 = 4 inches.

The height of the new rectangle would be 4 * 2 = 8 inches.

2) if a similar box has a width of 6 inches, it means that the ratio of its width to that of the original rectangle would be

6/2 = 3

The length of the new rectangle would be 3 * 3 = 9 inches.

The height of the new rectangle would be 4 * 3 = 12 inches.

3) if a similar box has a height of 6 inches, it means that the ratio of its height to that of the original rectangle would be

6/4 = 1.5

The length of the new rectangle would be 3 * 1.5 = 4.5 inches.

The width of the new rectangle would be 2 * 1.5 = 3 inches.