The diagonal of a rectangle is 8 cm longer than its shorter side. If the area of a rectangle is 60 square meter .find its dimension

the longer side is √((x+8)^2 - x^2) = √(16x+64) = 4√(x+4)

so now you know that
x*4√(x+4) = 60
so solve for x and then you can get 4√(x+4)

or, you can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.