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The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is (in square units)
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Verified Answer
The correct answer is:
8
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.
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