Question

if the sum of the lengths of the diagonals of a square is 144m then its area is​

Answer 1

$\huge\star\boxed{\mathfrak\pink{\underline{\underline{Answer}}}}\star$

$\textbf{ Area=2,591.217216\:m^2 }$

$\huge\star\star\boxed{\mathbb\red{\underline{\underline{GIVEN}}}}\star\star$

$\odot\:\:\textbf{Sum\:of\:Diagonals=144m}$

$\huge\star\star\star\boxed{\mathbb\green{\underline{\underline{TO\: CALCULATE}}}}\star\star\star$

$\odot\:\:\textbf{Area\:of\: square}$

$\huge\star\star\star\star\boxed{\mathcal\red{\underline{\underline{Explanation}}}}\star\star\star\star$

$\textsf{Let the side of a square be a. }$

$\boxed{\textsf{Diagonal of a square= \sqrt{2}a }}$

$\textsf{where a is the side of the square }$

$\huge\texttt{ATQ,}$

$\textsf{ 2\times\sqrt{2}a=144\:m }$

$\Longrightarrow\textsf{ \sqrt{2}a=72\:m }$

$\Longrightarrow\textsf{ a=\dfrac{72}{\sqrt{2}}\:m }$

$\textsf{We cannot substitute the value of \sqrt{2} because}$

$\textsf{we do not know the accurate value of \sqrt{2} }$

$\textsf{So we rationalise the denominator by multiplying}$

$\textsf{with \sqrt{2} with numerator and denominator}$

$\textsf{a= \dfrac{72}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}\:m }$

$\textsf{ a=\dfrac{72\:\times\:\sqrt{2}}{2}\:m }$

$\textsf{ a=36\sqrt{2}\:m }$

$\textsf{Substituting the value of \sqrt{2} as 1.414}$

$\Longrightarrow\textsf{ a=36\times1.414 m }$

$\Longrightarrow\textsf{ a=50.904 m }$

$\huge\boxed{\texttt{Area\:of\: Square}}$

$\boxed{\textbf{ Area\:of\: square\:=\:side^2\:or\:a^2 }}$

$\textsf{ Area=50.904^2\:m^2 }$

$\textsf{ Area=2591.217216\:m^2 }$

$\therefore\textbf{The\:Answer\:is\: 2591.216216\:{m}^{2} }$

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