TIFR CSE 2021 | Part A | Question: 2

Question

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 $1$)?

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. $5$

Comments

https://csedoubts.gateoverflow.in/28917/tirf-gs2021-question

Answer 1

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.