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Question Number 89097 by TawaTawa1 last updated on 15/Apr/20

Commented by mr W last updated on 15/Apr/20

$$\sqrt{5^2+{(10+5)}^2}=5\sqrt{10}$$$$s=5\sqrt{10}-\frac{5}{5\sqrt{10}}(15+5)=3\sqrt{10}$$$$area=s^2=9\times 10=90$$

Answered by $@ty@m123 last updated on 15/Apr/20

$$Letsidesoftherightangled△with$$$$hypotaneous5be$$$$xandywherey>x.Then$$$$x^2+y^2=5^2...\left(1\right)$$$$Letzbethesideofcolouredsquare.$$$$Then,$$$$\frac{x}{y}=\frac{y}{y+z}=\frac{5}{15}$$$$\frac{x}{y}=\frac{y}{y+z}=\frac{1}{3}$$$$\Rightarrow 3y=y+z\Rightarrow 2y=z...\left(2\right)$$$$\mathrm{\&}y=3x.....\left(3\right)$$$$From\left(1\right)\mathrm{\&}\left(3\right),$$$${\left(\frac{y}{3}\right)}^2+y^2=25$$$$\frac{y^2}{9}+y^2=25$$$$10y^2=25\times 9$$$$y^2=\frac{45}{2}...\left(4\right)$$$$\therefore From\left(2\right),$$$$z^2=4y^2$$$$\Rightarrow Areaofcolouredsquare=4\times \frac{45}{2}$$$$=90sq.unit$$

Commented by john santu last updated on 15/Apr/20

$$somethingwrongsir$$$$itshouldbe\frac{x}{y}=\frac{5}{15}=\frac{1}{3}$$$$y=3x\Rightarrow x^2+y^2=10x^2=25$$$$x^2=\frac{5}{2}\Rightarrow z=6x$$$$\Rightarrow z^2=36x^2=36\times \frac{5}{2}=90squnit$$

Commented by $@ty@m123 last updated on 15/Apr/20

$$Thanksforcorrection.$$$$Iamexpertincommittingsillymistakes.$$$$:):):)$$

Commented by john santu last updated on 15/Apr/20

$$⋮)⋮)hahaha$$

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