The sides of a rectangle are in the ratio4:5.by what fraction should the shorter side be increaaed tomake it a square

Strange wording.

"What fraction" of what should the shorter side be increased?

Since the sides are stated in a ratio, they could be
4 cm by 5 cm, 40 miles by 50 miles, 8 ft by 10 ft, etc
In each case the shorter side would be increased by 1/4 of its original length.

in its simples form, the side of 4 units must be increased by 1 unit to make it 5 units. It is now a square.
So it is increased by 1/4 of its own original length.