Question

The diagonal of square measures 10 units. Find the perimeter of the square?

Answer 1

P= `20sqrt2` units

Explanation:

A diagonal splits the square into `45-45-90` degree triangles, therefore:

Side opposite to 90 degrees: `xsqrt2`
Side opposite to 45 degrees: `x`
Side opposite to 45 degrees: `x`

And since the hypotenuse which is the diagonal is `10`:
`xsqrt2=10`
`x=10/sqrt2*sqrt2/sqrt2= (10sqrt2)/2 = 5sqrt2 "units"`

Perimeter of a square:
`P=4s`
`P=4( 5sqrt2 )`
`P=20sqrt2` units