Answer:

CASE 1

we have to DRAW square of area 13 cm².​

This implies

Side of square = √13 cm

We can write 13 as sum of squares of 3 and 2

13 = 3²  + 2²

first make a line PQ of  5 cm  with a Point A on it whose distance from P is 3CM

so

PA = 3 cm  QA = 2cm

Draw perpendiculars at P and Q on line PQ

draw at  perpendicular PD = 2cm  

and

QB = 3cm

Now join  AB  and AD

Now

AB = AD = √13 cm

And

Perpendicular to each other

Now Draw perpendicular on AD and AB  and produced them until they cut at C

Hence

ABCD square with Side = √13 cm  prepared

Case 2

Since we can write

7² - 6² = 13

make a line PA  = 6 cm

Draw perpendicular at A on line PA

Now by Using compass of Length 7 cm from P Cut Perpendicular from point A at  point D

we get AD = √13 cm

Now produce PA line

and

produce line DA  such that DQ = 6 cm

Now from point Q by Using compass draw 7 cm arc to Cut produced PA line at point B

we get AB = √13 cm

Now Draw perpendicular at AB

and

AD  

And

Produced them to meet at C

So we get ABCD Square Side√13 cm .