Take 36 square cards each of unit length. In how many ways can you put them together to form a rectangle? One is done for you. Which arrangement will make a rectangle of greatest perimeter and which arrangement will make a rectangle of least perimeter?
Answers
Given : 36 square cards each of unit length.
To Find : In how many ways can you put them together to form a rectangle
Solution:
36 square cards hence area of a rectangle = 36 sq cm
possible solutions are
1× 36 , 2 ×18 , 3×12 , 4×9, 6×6
calculate perimeters in each case
6 × 6 = 2(6 + 6) = 24 cm
4 × 9 = 2 ×(4+9) = 26 cm
3 × 12 = 2 ×(3+12) = 30 cm
2 × 18 = 2 × (2 + 18) = 40 cm
1 × 36 = 2 × (1+36) = 74 cm
greatest perimeter = 74 cm
minimum perimeter = 24 cm ( square make least perimeter)
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