This is a really good question
I haven't seen one quite like it before.
Let the length actually purchased be x m long.
so originally the cloth is 0.9m by x m
The cloth shrinks 10% in both directions so this means that after washing the length and width are each 90% of the original.
So after shrinking the width is 90% of 0.9 = 0.9*0.9 = 0.81m
The length is 90% of x = 0.9x
Now the shrunken area is 21.87m 2
0.81 * 0.9*x = 21.87m 2
x = 21.87/0.81/0.9
x = 30 metres