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Question Number 26036 by chand908 last updated on 18/Dec/17

Find the area of a square if the sum  of the diagonals is 100 cm.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{diagonals}\:\mathrm{is}\:\mathrm{100}\:\mathrm{cm}. \\ $$

Answered by mrW1 last updated on 18/Dec/17

2d=100  ⇒d=50 cm  ⇒a=(d/(√2))=((50)/(√2))  ⇒A=a^2 =(((50)/(√2)))^2 =((2500)/2)=1250 cm^2

$$\mathrm{2}{d}=\mathrm{100} \\ $$$$\Rightarrow{d}=\mathrm{50}\:{cm} \\ $$$$\Rightarrow{a}=\frac{{d}}{\sqrt{\mathrm{2}}}=\frac{\mathrm{50}}{\sqrt{\mathrm{2}}} \\ $$$$\Rightarrow{A}={a}^{\mathrm{2}} =\left(\frac{\mathrm{50}}{\sqrt{\mathrm{2}}}\right)^{\mathrm{2}} =\frac{\mathrm{2500}}{\mathrm{2}}=\mathrm{1250}\:{cm}^{\mathrm{2}} \\ $$

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