a-Determine-the-area-of-the-largest-rectangle-that-can-be-inscribed-in-the-circle-x-2-y-2-a-2-b-Name-the-rectangle-so-formed-

Question Number 56763 by Tawa1 last updated on 23/Mar/19

(a) Determine the area of the largest rectangle that can be

inscribed in the circle x^{2} + y^{2} = a^{2} .

(b) Name the rectangle so formed

Answered by kaivan.ahmadi last updated on 23/Mar/19

S = 4 x \sqrt{a^{2} - x^{2}} \Rightarrow S^{'} = 4 \sqrt{a^{2} - x^{2}} + \frac{- 4 x^{2}}{\sqrt{a^{2} - x^{2}}} =

\frac{4 a^{2} - 4 x^{2} - 4 x^{2}}{\sqrt{a^{2} - x^{2}}} = 0 \Rightarrow 8 x^{2} = 4 a^{2} \Rightarrow

x^{2} = \frac{a^{2}}{2} \Rightarrow x = \frac{a}{\sqrt{2}} \Rightarrow

S = 2 \sqrt{2} a \sqrt{a^{2} - \frac{a^{2}}{2}} = 2 \sqrt{2} a \sqrt{\frac{a^{2}}{2}} = 2 a^{2}

Commented by kaivan.ahmadi last updated on 23/Mar/19

Commented by Tawa1 last updated on 23/Mar/19

God bless you sir

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