Question

Rachel has 30 paper squares. Each square is 2 cm on a side. She arranges all of them, without overlapping, to form a rectangle. In centimeters, what is the smallest possible perimeter of the rectangle? What is the greatest possible perimeter?

Answer 1

The smallest possible perimeter of a rectangle formed by 30 squares of side 2cm is 124 cm, and the greatest possible perimeter is 44 cm .

Step-by-step explanation:

Rachel has 30 squares, each with a side length of 2 cm. When arranged in a rectangle, the smallest possible perimeter would be achieved by creating a rectangle with the dimensions 30 x 2cm (taking advantage of all 30 squares in a single line). This would give us a perimeter of (2+60)*2 = 124 cm (since perimeter is 2*(length + width)).

The largest possible perimeter would be achieved with a rectangle that is very nearly a square, balancing the length and width as equally as the number of squares allows. The closest we can come to a perfect square shape would be a rectangle with dimensions 5 x 6 squares (since 5 and 6 are the factors of 30 that are closest to each other). This yields dimensions of 10 cm x 12 cm, and a perimeter of (10+12)*2 = 44 cm.

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