A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct? I. The rectangle of the largest area is the square. II. It is possible to form a rectangle of an area of 27 cm^2. Select the answer using the code given below.
A. I only
Let the length and breadth of the rectangle be x and y respectively. Given the perimeter of the rectangle is 20 cm . 2(x + y) = 20 x + y = 10 The area of the rectangle is A = xy. Substituting y = 10 - x, we get: A = x(10 - x) = 10x - x^2 To find the maximum area, we can complete the square: A = 25 - (x - 5)^2 The maximum value of A is 25 cm ^2, which occurs when x = 5 cm . When x = 5 cm , y = 10 - 5 = 5 cm . Since x = y, the rectangle of the largest area is a square. Thus, statement I is correct. The maximum possible area is 25 cm ^2. It is not possible to form a rectangle of area 27 cm ^2. Thus, statement II is incorrect. Only statement I is correct. Answer: I only
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