Question

Construct a square with a diagonal of length 6cm

Answer 1

As per the given question: 
Side = 6 cm 
Since we know that all sides of square are equal in length, so we get: 
PQ = QR = RS = SP = 6 cm each 

Also, we know that in a square all vertices form 90 degree angle, so we get 
Angle A + Angle B + Angle C + Angle D = 90 degree each 

Steps of construction are as follows: 

Step 1: Draw a line segment PQ of 6 cm.

Step 2: With the help of compass draw 90 degree angle at P.
(To study how to construct 90 degree angle with the help of compass) 

Step 3: With the help of compass draw 90 degree angle at Q.
(To study how to construct 90 degree angle with the help of compass) 

Step 4: Use compass and 6 cm wide open. With P as center, draw an arc; which cuts arms of 90 degree angle. And mark point of intersection as S.

Step 5: Use ruler and measure length of SP. Length of SP should be 6 cm and we get: 

Step 6: Again Use compass and 6cm wide open. With Q as center, draw an arc; which cuts arms of 90 degree angle. And mark point of intersection as R.  

Step 7: Use ruler and measure length of RQ. Length of RQ should be 6cm and we get: 

Step 8: Join points S & R

Step 9: Use ruler and measure length of SR. Length of SR should be 6cm and we get resultant square PQRS: 

*I HOPE YOU GET THIS*