A square has an area of 200, m^2. A new squar | vedclass

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(C) The side of the first square is $\sqrt{	ext{Area}} = \sqrt{200} = 10\sqrt{2}\, m$.The diagonal of the first square is $\sqrt{2} 	imes 	ext{side

Vedclass · Accepted Answer

$400$

Vedclass · Answer

(C) The side of the first square is $\sqrt{	ext{Area}} = \sqrt{200} = 10\sqrt{2}\, m$.The diagonal of the first square is $\sqrt{2} 	imes 	ext{side} = \sqrt{2} 	imes 10\sqrt{2} = 20\, m$.The diagonal of the new square is $\sqrt{2} 	imes 20 = 20\sqrt{2}\, m$.The area of a square is given by $\frac{1}{2} 	imes (	ext{diagonal})^2$.Therefore,the area of the new square is $\frac{1}{2} 	imes (20\sqrt{2})^2 = \frac{1}{2} 	imes 400 	imes 2 = 400\, m^2$.

$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?

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