Consider all rectangles that can be made with a 1 metre long rope.
Take one of its sides as x centimetres and the area enclosed as a (x)
square centimetres.
1) Write the relation between a (x) and x as an equation.
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a(x) = 50x - x² a = area of rectangle , x is one side , perimeter = 1 m
Step-by-step explanation:
One of side of Rectangle = x centimetres
1 meter = 100 cm
Length of rope = Perimeter = 100 cm
Another Side of Rectangle = (100 - 2x)/2 = 50 - x cm
Area of Rectangle = x (50 - x)
=> a(x) = 50x - x²
Additional info :
da/dx = 50 - 2x
=> 50 - 2x = 0
=> x = 25
d²a/dx² = -2
=> Area of rectangle will be maximum when x = 25 => 50-x = 25
Hence Area of rectangle for given perimeter is maximum when its square
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