why is this 5 rad 2?

Question

Find in radical form the length of a diagonal of a square if the perimeter of a square is 20.

Answer 1

A square has 4 equal sides.
This square's perimeter (distance around) is 20.
Therefore each side =5
The diagonal is the hypotenuse of a right triangle
whose sides are each 5.
Therefore the hypotenuse, and therefore the diagonal,
obey the Pythagorean theorem.
H^2=sq.rt.{(5)^2+(5)^2}
H^2=sq.rt{25+25}
H^2=sq.rt.(50)
H=5sq.rt.2

Answer 2

if the perimeter of a sq = 20, then each side = 5
using a^2+b^2=c^2

the diagonal = sqrt(5^2 + 5^2) = sqrt(50) = 5 sqrt(2)

Answer 3

let each side of a square be 'a'
the diagnol joins the opposite vetrices of a square and divide square into two equal right angle triangles.
let the diagnal be 'b'.
since all sides are equal to 'a'and both diagnals are equal to 'b'

now apply right angle triangle property:
b^2=(a^2)+(a^2)=2(a^2)
then b=sqrt(2(a^2))=(sqrt(2)*(a))

but perimeter of a square=4a=20(given) then a=5

therefore diagnol of a squre is b=sqrt(2)*(5)=sqrt(50)

Answer 4

length of side = 5
d² = 5² + 5²
d² = 50
d = √50
d = √(25 x 2)
d = 5 √2