A rectangle has an area 18cm square. if it's length and width are whole numbers, what is it's greatest possible perimeter show full solution
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Let's say its length is X cm
Therefore it's width is (18/X) cm
Perimeter is 2×(L + B)
= 2×(X + 18/X)
P = 2X + 36/X
(dP/dX) = 2 - 36/X^2 = 0
Which gives X = ✓18 but this is not a whole number. X = 4.242
So we take the nearest number for which both X and 18/X are whole numbers
Which is 3
Hence Length is 6 cm, Breadth is 3 cm and Perimeter is 18cm
Therefore it's width is (18/X) cm
Perimeter is 2×(L + B)
= 2×(X + 18/X)
P = 2X + 36/X
(dP/dX) = 2 - 36/X^2 = 0
Which gives X = ✓18 but this is not a whole number. X = 4.242
So we take the nearest number for which both X and 18/X are whole numbers
Which is 3
Hence Length is 6 cm, Breadth is 3 cm and Perimeter is 18cm
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