from a rectangular carboard ,36 squares of side 1cm can be cut off.what are the possible lengths and widths in centimetres,if both are to be natural numbers?
Answers
L= 12 B=3
L= 6 B=6 (Square)
L= 9 B=4
L=18 B=2
The possible lengths and widths of the cardboard in centimeters are:
(1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), and (18, 2).
If 36 squares of side 1cm can be cut off from rectangular cardboard, then the total area of the cardboard must be equal to 36 square cm. This means that the length and width of the cardboard must multiply by 36.
Since both the length and width have to be natural numbers, we can find all the possible pairs of numbers that multiply to 36 by listing all the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.
Therefore, the possible lengths and widths of the cardboard in centimeters are: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6), (9, 4), (12, 3), and (18, 2). These are all the pairs of natural numbers that multiply to 36 and represent the possible dimensions of the cardboard.
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