Question

The diagonal of a square is
$4 \sqrt{2}$
then find the following:
(i) Length of each side
(ii) Perimeter of square​

Answer 1

Answer:

Answer:

side = 4 cm

perimeter = 16 cm

Step-by-step explanation:

Let s be the length of a side of the square.

Two sides and the diagonal together make a right angled triangle with the diagonal as hypotenuse. So by Pythagoras' Theorem:

s² + s² = (square of diagonal) = (4√2)² = 4² × √2² = 16 × 2 = 32

=> 2s² = 32

=> s² = 16

=> s = 4.

So the side of the square has length 4cm.

The perimeter is then:

perimeter = 4 × side = 4s = 4 × 4cm

=> perimeter = 16cm.