Question

Find the perimeter of square, if its diagonal is 2√2​

Answer 1

Answer:

P=5.66

Step-by-step explanation:

P=4a

d=2a

Solving forP

P=22d=2·2·2≈5.65685

Answer 2

Given:

A square with a diagonal 2√2​

To Find:

Find the perimeter of the square

Solution:

A square is a 2-D figure with sides in which all the four sides are equal and each adjacent side has 90 degrees of angle between them. The two diagonals of a square are also equal in length,

To find the perimeter of a square with sides of length 'a' we use a formula as

$P=4a$

And in the given question it says that the square has a diagonal of 2√2​ so the value of sides can be found by, if a diagonal is drawn then the square separates into two equal right-angled triangles with the base and perpendicular as the sides and the hypotenuse as diagonal,

Applying the Pythagoras theorem, we have

$a^2+a^2=(2\sqrt{2})^2\\2a^2=8\\a^2=4\\a=\pm2$

As the value of sides cannot be negative, so a=2

Now the perimeter of the square will be,

$P=4a\\=4*2\\=8$

Hence, the perimeter of the square is 8.