Find the side and perimeter of a square whose diagonal is `10cm`.

Explanation

Let `square ABCD` be the given square.
`AC=10cm`
Let the side of the square be `x cm`
In `DeltaABC`,
`/_ABC=90^(@)`………(Angle of a square)
`:.` by Pythagoras theorem,
`AC^(2)=AB^(2)+BC^(2)`
`:.10^(2)=x^(2)+x^(2)`
`:.100=2x^(2)`
`{:( :.x^(2)=(100)/(2), :. x^(2)=50, :. x=5sqrt(2)):}`
`:.AB=5sqrt(2)cm`. `:.` side of square is `5sqrt(2)cm`.
Perimeter of a square `=4xx` side
`=4xx5sqrt(2)`
`=20sqrt(2)cm`