Question

The diagonal of a square is x what is the perimeter of the square

Answer 1

2
`√(2)` x

Explanation:

The diagonal divides the square into 2 right angles with legs s and hypotenuse x

Using Pythagoras' identity on one of the right triangles, then

s² + s² = x²

2s² = x² ( divide both sides by 2 )

s² =
`(x^2)/(2)` ( take the square root of both sides )

s =
`\sqrt{(x^2)/(2) }` =
`(x)/(√(2) )`

Thus

perimeter = 4s = 4 ×
`(x)/(√(2) )` =
`(4x)/(√(2) )`

Multiply numerator/ denominator by
`√(2)`

perimeter =
`(4x√(2) )/(2)` = 2
`√(2)` x