Question

area of square is 100 cm2 find diagonal of square?

Answer 1

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!}}}$

$<b><i><font face=Copper black size=4 color=blue>$ Here is your answer.

Let the side is x cm

Area of Square= side^2
${x}^{2} = 100 \\ x = \sqrt{100} \\ x = 10$
For finding diagonal we use Pythagoras Theorem
Side = 10 cm
Let Diagonal is y cm
so
${y}^{2} = 10 {}^{2} + 10 {}^{2} \\ {y}^{2} = 100 + 100 \\ {y}^{2} = 200 \\ y = \sqrt{200} \\ y = 10 \sqrt{2} \: cm$

Therefore Diagonal of the square is 10√2 cm

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope \: it \: helps \: you}}}}}}}}}}}}}}}$p

Answer 2

Hi. Since a square is a rhombus with all it angles as right angles, area of square = 1/2 * diagonal1 * diagonal2. But, we know that the diagonals of a square are equal.

So, area of square = 1/2 * diagonal * diagonal.

Given area = 100 cm^2

Thus, 1/2 * diagonal^2 = 100

or, diagonal^2 = 100*2 = 200

or, diagonal = √200 = 14.14 cm approx

Hope it helps!