Question

The perimeter of a square is 56 cm what is the approximate length of its diagonal

Answer 1

The approximate length of diagonal is:

19.796 cm.

Explanation:

We are given the perimeter of a square as 56 cm.

Let 's' be the side of the square.

We know that the perimeter of square is given as:

`Perimeter=4* s\\\\56=4s\\\\s=(56)/(4)\\\\s=14`

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:
`D=√(2)s`

( Since it could be proved with the help of Pythagorean Theorem )

Hence, as s=14 cm

Hence, the length of diagonal is:

`D=√(2)* 12\\\\D=1.414* 14\\\\D=19.796\ cm`

Hence, the approximate length of diagonal is:

19.796 cm.

Answer 2

perimeter = 4s

56=4s

s=56/4 = 14

diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm

round answer as needed