How many different rectangles of different perimeters can be formed by rearranging sixteen square tiles arranged as shown below. Find their perimeters, if the side of each square tile is 1 cm.

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Solution

By rearranging 16 tiles, two different rectangles of different perimeters can be formed as shown below.
Perimeter of rectangle 1 = 2 $\times$ 8 + 2 $\times$ 2 = 20 cm
Perimeter of rectangle 2 = 2 $\times$ 16 + 2 $\times$ 1 = 34 cm

Note: In all the arrangements the area is same, 16 sq. cm.

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How many different rectangles of different perimeters can be formed by rearranging sixteen square tiles arranged as shown below. Find their perimeters, if the side of each square tile is 1 cm.

By rearranging 16 tiles, two different rectangles of different perimeters can be formed as shown below. Perimeter of rectangle 1 = 2 × 8 + 2 × 2 = 20 cm Perimeter of rectangle 2 = 2 × 16 + 2 × 1 = 34 cm Note: In all the arrangements the area is same, 16 sq. cm.

By rearranging 16 tiles, two different rectangles of different perimeters can be formed as shown below.
Perimeter of rectangle 1 = 2 $\times$ 8 + 2 $\times$ 2 = 20 cm
Perimeter of rectangle 2 = 2 $\times$ 16 + 2 $\times$ 1 = 34 cm

Note: In all the arrangements the area is same, 16 sq. cm.