Question

find the perimeter of a square whose diagnol is 5 root 2 cm

Answer 1

Diagonal-5√2

Since square has equal all sides and each angle is 90°

so, when it draw diagonal

It will form right angle triangle whose hypotenuse will be diagonal..

Now

let side os square be x

so,
${x}^{2} + {x}^{2} = {d}^{2} \\ d = diagonal \\ 2 {x}^{2} = {(5 \sqrt{2} )}^{2} \\ 2 {x}^{2} = 25 \times 2 \\ {x}^{2} = 25 \\ x = + 5 \: and \: - 5 \\ since \: it \: is \: side \: so \: we \: reject - 5$
now side of square is 5

◆perimeter=4×sides

=>4×5=20units

perimeter of square is 20 units.