Question

Of all rectangles each of which has perimeter 24 cm find that one having maximum area also find its area

Answer 1

Step-by-step explanation:

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Answer 2

The area of the rectangle = 36 cm²

Let the length of the rectangle = x

Let the breadth of the rectangle = y

Given , perimeter = 24

=> 2(x + y) = 24

=> x + y = 12

Area of the rectangle = A = xy

=> A = x (12-x) [substituting the value of y from the value of perimeter]

=> A = 12x - x²

Let A be a function f(x) and f(x) =

12x - x²

Differentiating f(x) with respect to x

=> f'(x) = 12 - 2x

The value of the function f(x) will be maximum for f'(x) = 0

=> 12 - 2x = 0

=> x = 6

y = 12 - x = 6

The rectangle will be a square of side 6 cm ( a square is a special type of rectangle ).

The area of the rectangle = xy

= 36 cm²