KCET · Maths · Application of Derivatives
The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in square unit)
- A 4
- B \(8 \pi\)
- C 8
- D 5
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
The maximum area of a rectangle that inscribedThe maximum area of a rectangle that inscribed in a circle is equal to the area of square whose diagonal length is 4 unit.
Let the side of square be \(x\) unit. \( \begin{array}{ll} \therefore & (4)^{2}=x^{2}+x^{2} \\ \Rightarrow & 2 x^{2}=16 \\ \Rightarrow & x^{2}=8 \text { sq unit } \end{array} \) in a circle is equal to the area of square whose diagonal length is 4 unit.
Let the side of square be \(x\) unit. \( \begin{array}{ll} \therefore & (4)^{2}=x^{2}+x^{2} \\ \Rightarrow & 2 x^{2}=16 \\ \Rightarrow & x^{2}=8 \text { sq unit } \end{array} \)
Let the side of square be \(x\) unit. \( \begin{array}{ll} \therefore & (4)^{2}=x^{2}+x^{2} \\ \Rightarrow & 2 x^{2}=16 \\ \Rightarrow & x^{2}=8 \text { sq unit } \end{array} \) in a circle is equal to the area of square whose diagonal length is 4 unit.Let the side of square be \(x\) unit. \( \begin{array}{ll} \therefore & (4)^{2}=x^{2}+x^{2} \\ \Rightarrow & 2 x^{2}=16 \\ \Rightarrow & x^{2}=8 \text { sq unit } \end{array} \)
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