If diagonal of a square is 13 cm then find its side.
Ratio of two adiacent sides​

2 thoughts on “<br />If diagonal of a square is 13 cm then find its side.<br />Ratio of two adiacent sides​”

1. Appropriate Question :

   • If diagonal of a square is 13 cm then find the side of a Square .

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   Given : The Diagonal of Square is 13 cm .

   Need To Find : Length of Side of Square.

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   [tex]\dag\:\;\frak {\underline { As,\:We\:know\:that\::}}\\\\[/tex]

   [tex]\dag\:\:\boxed {\sf{ Diagonal_{(Square)} =\bigg( \sqrt {2} a\bigg) }}\\\\[/tex]

   Where,

   • a is the Side of Square.

   ⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}\\[/tex]

   [tex] :\implies\sf{13 = \sqrt {2} a}\\\\ :\implies\sf{a= \dfrac{13}{\sqrt{2}}}\\\\:\implies\sf{a= \dfrac{13\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}}\\\\:\implies\sf{a= \dfrac{13\sqrt{2}}{2}}\\\\:\implies\sf{a= \dfrac{\cancel {13}\sqrt{2}}{\cancel {2}}}\\\\\qquad \quad \underline {\boxed{\purple{ \frak { a = 6.5\sqrt {2}\: cm}}}}\:\bf{\bigstar}\\[/tex]

   Therefore,

   ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence,\:Side \:of\:Square \:is\:\bf{6.5\sqrt {2}\: cm}}}}\\[/tex]

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2. ✩ We know that :

   Diagonal of 3 square is given as 13 cm.

   ✩ Let a be the side of the square.

   Diagonal = 13

   　　　　[tex] \large \sf = \sqrt{2a} = 13[/tex]

   　　　　[tex] \large \sf a \: = \frac{13}{ \sqrt{2} } [/tex]

   　　　　[tex]\large \sf a = \frac{13 \sqrt{2} }{2} [/tex]

   　　　　[tex]\large \sf a \: = 6.5 \sqrt{2} cm[/tex]

   　　　　[tex]\large{\underline{\boxed{\mathfrak\pink{a \: = 6.5 \sqrt{2} \: cm}}}}[/tex]

   Therefore, the length of the side of the square is 6 .

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