Q111 / 180 · COMEDK 2019 · Mathematics
The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is (in square units)
- A4
- B$8 \pi$
- Correct answerC8
- D5
Solution
The area of a rectangle that can be inscribed in a circle will have maximum area when it is a square.
Let $a$ be the side of square $A B C D$. Then, $$ \begin{aligned} A B^{2}+B C^{2} &=A C^{2} \\ a^{2}+a^{2} &=(4)^{2} \\ 2 a^{2} &=16 \\ a^{2} &=8 \end{aligned} $$ $\therefore$ Area of square is $8 \mathrm{sq}$ units.
Let $a$ be the side of square $A B C D$. Then, $$ \begin{aligned} A B^{2}+B C^{2} &=A C^{2} \\ a^{2}+a^{2} &=(4)^{2} \\ 2 a^{2} &=16 \\ a^{2} &=8 \end{aligned} $$ $\therefore$ Area of square is $8 \mathrm{sq}$ units.
Hence, the correct answer is option: 'C'.