Question

If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square

Answer 1

Answer:

The perimeter of the square is $31.96\ m$

Step-by-step explanation:

we know that

The perimeter of a square is equal to

$P=4b$

where

b is the length side of the square

Step 1

Find the length side of the square

The diagonal of the square is equal to

Applying the Pythagoras Theorem

$d^{2} =b^{2}+b^{2}\\d^{2}=2b^{2}\\d=b \sqrt{2}$

In this problem we have

$d=11.3\ m$

$d=b\sqrt{2}$ ------> solve for b

$b=d/\sqrt{2}$

substitute the value of d

$b=11.3/\sqrt{2}\ m$

Step 2

Find the perimeter of the square

$P=4b$

Substitute the value of b

$P=4(11.3/\sqrt{2})=31.96\ m$

Answer 2

The length of each side can be found using pythagoras theorem:-

11.3^2 = 2x^2     where x = length od each side
x = sqrt( [11.3^2  / 2)
x =  7.99 meters