Question

the area of a square is 25 square
cm find the length of it's diagonal

Answer 1

side = √25

so side is = 5 cm

diagonal is = √2 × side

so diagonal = 5√2 cm answer...

Answer 2

$\fcolorbox{blue}{white} { \red{Solution:-} }$

$\red{given:-} \: area \: of \: square \: is \: 25 {cm}^{2} \\ \\ as \: we \: know \: diagonal \: of \: square \: \\ are \: equal \: and \: all \: angle \: of \: square \: are \: of \: {90}^{0} .$

$\blue{Area \: of \: square } = \red{ {side}^{2} } \\ \\ 25 = \red{ {side}^{2} } \\ \green {i.e.} \\ \\ \red{ {side}^{2} } = 25 \\ \\ \red{side} = \sqrt{25} \\ \\ \red{side} = 5 \\ \\ \fcolorbox{red}{white}{ now \: by \: pythagorus \: theorem} \\ \\ \red {{hypotenuse}^{2} = { ({1}^{st} side)}^{2} + { ({2}^{cd}side) }^{2} } \\ \\ \red {{hypotenuse}^{2} = ({5})^{2} + ({5})^{2} } \\ \\ \red {{hypotenuse}^{2} = 25 + 25 } \\ \\ \red {{hypotenuse}^{2} = 50 } \\ \\ \red {{hypotenuse} = \sqrt{50} } \\ \\ \red{ hypotenuse = \sqrt{5 \times 5 \times 2} } \\ \\ \red{ hypotenuse = 5\sqrt{2} }$

$\fcolorbox{red}{aqua} {hence \: diagonal \: of \: square\: } = \red{5 \sqrt{2} \: cm }$

$\fcolorbox{red}{white} {i \: hope \: it \: helps \: you.}$