Square paper sheets of two sizes are needed for an art project. How many of the smaller sheets are needed to cover one of the larger sheets if it is known that the perimeter of one of the larger sheets is eight times as great as the perimeter of one of the smaller sheets?

64 sheets

Step by step:
Given x to be the length of one side of the smaller square sheet, the perimeter of the smaller sheet would be 4x. Because the larger sheet’s perimeter is eight times as great as the smaller sheet, the smaller sheet’s perimeter multiplied by eight is the larger sheet’s perimeter. 4x multiplied by eight is 32x.

To find the length of a side from the larger sheet, divide the perimeter by four (number of sides a square sheet has) resulting in the larger sheet’s side being 8x. One side of the smaller sheet is x, as stated before.

Substituting 1 for x, how many 1 by 1 squares can fit in an 8 by 8 square? 8 smaller squares can fit on each side of the larger square. So, to find the area in terms on number of smaller sheets multiply 8 by 8. Therefore, 64 smaller sheets fit in one larger sheet.