Question

Resna said only one square can be drawn having a diagonal of 5cm is it true explain

Answer 1

let a be the side of the square.  Then its diagonal is given by the pythagoras theorem,

   diagonal² = a² + a² = 2 a²
  diagonal = √2 a  = 5 cm
   => side = a = 5/√2 cm = 2.5 √2 cm
 
hence, there is only one square is possible with a diagonal of 5 cm .

Answer 2

Let s =  side of the square.

Diagonal² = s² + s² = 2 s²
Diagonal =
 √2 s  = 5 cm
 s = $\frac{5}{ \sqrt{2} }$ 
s = $\frac{5 \sqrt{2} }{2}$
 
Hence, only one square is possible with a diagonal of 5 cm .