Question

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

Answer 1

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

Answer 2

Answer:

The approximate length of diagonal is:

19.796 cm.

Step-by-step 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:

$Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14$

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:$D=\sqrt{2}s$

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

Hence, as s=14 cm

Hence, the length of diagonal is:

$D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm$

Hence, the approximate length of diagonal is:

19.796 cm.