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Answer :
Final answer:
The possible length and width of the rectangle are the factor pairs of 120: (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), and (10,12). Among these pairs, the pair (10,12) gives the smallest perimeter.
Explanation:
The area of a rectangle is calculated by multiplying its length and width. Given that the area is 120 cm2 and the length and width are whole numbers, we determine the factor pairs of 120. The factor pairs of 120 are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), and (10,12).
The perimeter of a rectangle is calculated as 2(length+width). Therefore, of all the pairs, the pair that has the smallest sum (length+width) will give the smallest perimeter. In this case, the numbers 10 and 12 give the smallest sum and hence, the smallest perimeter.
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The two numbers can be any factors of 120. This includes: (1,120) (2,60)(3,40)(4,30)(5,24)(6,20)(8,15)(10,12) and the reverse of this. The smallest perimeter would be the two numbers that are closer together, which is 10 and 12.
