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Question Number 74112 by TawaTawa last updated on 19/Nov/19

Answered by mind is power last updated on 19/Nov/19

let l=side of squar⇒l^2 +(l/2)(x+z+y)=(((z+l+y))/2)(l+x)  ⇔2l^2 +l(x+y+z)=l(z+y+l)+x(z+l+y)  ⇒2l^2 +l(x+y+z)=l(x+y+z)+l^2 +xz+xy  ⇔l^2 =x(z+y)=area

$${let}\:{l}={side}\:{of}\:{squar}\Rightarrow{l}^{\mathrm{2}} +\frac{{l}}{\mathrm{2}}\left({x}+{z}+{y}\right)=\frac{\left({z}+{l}+{y}\right)}{\mathrm{2}}\left({l}+{x}\right) \\ $$$$\Leftrightarrow\mathrm{2}{l}^{\mathrm{2}} +{l}\left({x}+{y}+{z}\right)={l}\left({z}+{y}+{l}\right)+{x}\left({z}+{l}+{y}\right) \\ $$$$\Rightarrow\mathrm{2}{l}^{\mathrm{2}} +{l}\left({x}+{y}+{z}\right)={l}\left({x}+{y}+{z}\right)+{l}^{\mathrm{2}} +{xz}+{xy} \\ $$$$\Leftrightarrow{l}^{\mathrm{2}} ={x}\left({z}+{y}\right)={area} \\ $$$$ \\ $$

Commented by TawaTawa last updated on 19/Nov/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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