Question

Construct a square of diagonal $2\sqrt{2}$ cm long and calculate its perimeter in cm.

• A. $16$
• B. $4$
• C. $8$
• D. None of these

Answer 1

The correct option is C $8$

Suppose side of square is $x$

Applying Pythagoras theorem in triangle ABC

${AC}^2={AB}^2+{BC}^2{\left(2\sqrt{2}\right)}^2=x^2+x^{2}x=2$

Therefore, side of the square is $2$ cm

Draw a line segment $AB=2cm$

Draw angles of ${90}^o$ from $A$ and $B$

Draw arcs from $A$ and $B$ which cuts the perpendiculars at $D$ and $C$ respectively.

Join $CD$

$ABCD$ is the required square

So, perimeter will be

$=4\times x=4\times 2=8$

Hence, correct answer is option C.