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What is the area of a rectangle with the largest perimeter that can be inscribed in the unit circle (i.e., all the vertices of the rectangle are on the circle with radius $1$)?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$
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The answer will be option B) 2.

Solution :

              For max area, the rectangle will be a square. So, if x is the side of the square, we have

                  $x^2 + x^2 = (2(1))^2$

             Here, the diagonal of the square will be equal to the diameter of the circle.

            Solving this, we get $x = \sqrt{2}$ or the area of the square as 2 sq.units.
Answer:

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