One side of a rectangle is 1m less than the length of the diagonal. If the area of the rectangle is 60m squared , what are its dimension.

Assign variables.

Let l be the length of the rectangle.
Let w be the width of the rectangle.

The diagonal is obtained through the Pythagoras' Theorem,

Diagonal = \sqrt{l^2 + w^2}

Let the length be less than the diagonal

\sqrt{l^2 + w^2} - 1 = l

The area is lw = 60

Can you take it from here?