If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:

10%

Let the side of the square = 10

Now the area = 10²  = 100

Then the diagonal = 10\(\sqrt {2}\)  

According to the question if the area is decreased by 19% then the area = 81 and the side = 9

Now the diagonal = 9\(\sqrt {2}\) 

The change in the diagonal = 10\(\sqrt {2}\) -  9\(\sqrt {2}\) = \(\sqrt {2}\) 

= \(\frac{\sqrt {2} × 100}{10\sqrt {2}}\) = 10%