Question

The ratio of the area of two square with sides 4 cm and 8 cm is one of the following
1) 1:2
2) 1:4
3) 2:3
4) 1:12
also pls tell the solution ​

Answer 1

Given that , The sides of two square are 4 cm and 8 cm respectively .

Exigency To Find : Ratio of Area of two squares .

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We'll Firstly find Area of two Squares ( i.e. of side 4 cm and 8 cm ) , then we can easily find the ratio of there area . Formula to Find Area of Square is given by —

$\qquad \dashrightarrow \pmb{\purple{\sf Area_{\:(\:Square\:)}\:=\: Side^2\:}}$

⠀⠀⠀⌬⠀ Area of First Square ( side : 4cm ) —

$\qquad \longrightarrow \sf Area_{\:(\:Square\:1\:)}\:=\: Side^2\:\\\\ \longrightarrow \sf Area_{\:(\:Square\:1\:)}\:=\: 4^2\:\\\\ \longrightarrow \sf Area_{\:(\:Square\:1\:)}\:=\: 16\:\\\\\longrightarrow\pink{\pmb{\underline{\boxed{\frak{16\:cm^2\:}}}}}\:\bigstar\:$

⠀∴⠀Area of Square 1 is 16 cm² .

⠀⠀⠀⌬⠀ Area of Second Square ( side : 8 cm ) —

$\qquad \longrightarrow \sf Area_{\:(\:Square\:2\:)}\:=\: Side^2\:\\\\ \longrightarrow \sf Area_{\:(\:Square\:2\:)}\:=\: 8^2\:\\\\ \longrightarrow \sf Area_{\:(\:Square\:2\:)}\:=\: 64\:\\\\\longrightarrow\pink{\pmb{\underline{\boxed{\frak{64\:cm^2\:}}}}}\:\bigstar\:$

⠀∴⠀Area of Square 2 is 64 cm² .

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$\qquad\underline{\bigstar \:\:\pmb{\sf {\: Ratio\:of \: Area \::\:}}}$

$\twoheadrightarrow \sf\:Ratio\:_{\:(Area)}\:=\:\dfrac{ Area_{\:Square\:1}\:}{Area_{\:Square\:2}\:}\:\\\\ \twoheadrightarrow\sf \:Ratio\:_{\:(Area)}\:=\:\dfrac{ 16\:}{\:64\:}\:\\\\\twoheadrightarrow\sf \:Ratio\:_{\:(Area)}\:=\:\cancel{\dfrac{ 16\:}{\:64\:}}\:\\\\\twoheadrightarrow\sf \:Ratio\:_{\:(Area)}\:=\:\dfrac{ 1\:}{\:4\:}\:\\\\\twoheadrightarrow \pmb{\sf\:Ratio\:_{\:(Area)}\:=\:1:4 }\:$

∴ Ratio of Area of two Square is Option B ) 1 : 4 .