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

Answer

Side of a square is ` 5sqrt(2)` cm and
its perimeter is `20sqrt(2)` cm .

Explanation

` therefore ` by Pythagoras theorem,
` AC^(2) = AB^(2) + BC^(2)`
` therefore 10^(2) = x^(2) + x^(2)`
` therefore 100 = 2x^(2)`
` therefore x^(2) = (100)/(2)`
` therefore x^(2) = (100)/(2) `
` therefore x^(2) = 50`
` x = 5sqrt(2)`
` therefore AB = 5sqrt(2) ` cm .
` therefore ` side of square = 4 ` xx` side
` = 4xx5sqrt(2)`
` = 20sqrt(2)` cm