Question

if a diagonal of a square is 5.^2 find its side..​

Answer 1

Given: Diagonal of a square is 5² i.e 25 m.

❍ Lets consider Side of square be x m.

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☯ Let's Consider ABCD is a square.

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We know that,

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$\bigstar\:{\underline{\boxed{\sf{\purple{Pythagoras \: theorm_{\:(square)} = AB^2 + BC^2 = AC^2 }}}}}$

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$\dashrightarrow \sf {x}^{2} + {x}^{2} = {25}^{2}$

$\\ \dashrightarrow \sf {x}^{2} + {x}^{2} = 625$

$\\ \dashrightarrow \sf {2x}^{2} = 625$

$\\ \dashrightarrow \sf {x}^{2} = \dfrac{625}{2}$

$\\ \dashrightarrow \sf {x}^{2} = 312.5$

$\\ \dashrightarrow \sf {x} = \sqrt{312.5}$

$\\\\ :\implies{\underline{\boxed{\pmb{\frak{\pink{x = 17.67(Approx) }}}}}}\:\bigstar$

Hence,

⠀⠀▪︎⠀ Value of x is $\sf 17.67$

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$\therefore\:{\underline{\sf{Side\:of\:square\:is\:{\pmb{\frak{\purple{17.67 }}}}}}}$

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large x\ m}\put(4.4,2){\bf\large x\ m}\end{picture}$

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Answer 2

Given :- The diagonal of a square is 5² = 25 unit.

To find :- Side of the given square .

Used concepts :-

:- Pythagoras theorem.

:- All angles of a square are equal and of 90°.

:- Hypotenuse is the side opposite to the 90° angle .

:- All sides of a square are of same length .

Solution :-

We take the diagonal of the square as Hypotenuse because as it is opposite to the 90° angle . We also take base and perpendicular of same length " x " because All sides of the square are same .

Let,

Base of the right angled triangle ( B ) = x unit

Perpendicular of the right angled triangle ( P ) = x unit .

Hypotenuse of the right angled triangle ( H ) = 25 unit .

Now , By Pythagoras theorem ,

B² + P² = H²

x² + x² = (5²)²

2x² = 625

x² = 625/2

x² = 312.5

x= √312.5

Therefore , side of the given square is √ 312.5