AP EAMCET202125 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The maximum area of a rectangle that can be formed with a fixed perimeter of 20 units is sq units

Options

Correct answer

B. 25

Step-by-step solution

Let the sides of rectangle is x and y . Given, aligned 20 & =2(x+y) x+y=10 A & =x y=x(10-x)=10 x-x^2 d A d x & =10-2 x d A d x & =0 10-2 x=0 x & =5 d^2 A d x^2 =-2 < 0 aligned Area of rectangle is maximum when x=y=5 Area of rectangle =(5)^2=25

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