On a centimeter squared paper, make as many rectangles as you can, such that
the area of the rectangle is 64 sq.cm(consider only natural number lengths).
(1) Which rectangle has the greatest perimeter?
(ii) Which rectangle has the least perimeter?
(111) Find the change in width of rectangle with decreasing perimeter of
the rectangle.
Answers
Given : area of the rectangle is 64 sq.cm
To find : As many Rectangle as possible considering only natural number lengths
Solution:
Area = Length * Breadth
Area = 64 cm²
64 = 1 * 64
64 = 2 * 32
64 = 4 * 16
64 = 8 * 8
Length Width Perimeter ( all in cm)
1 64 130
2 32 68
4 16 40
8 8 32
16 4 40
32 2 68
64 1 130
Rectangle has greatest perimeter when Difference in Length & width is Greatest
Rectangle has the least perimeter when Difference in Length & width is Least ( means zero) hence when rectangle is Square
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