That is a big chocolate!

Since all of the angles of a rectangular cake are $90^\circ,$ we can draw a right triangle with sides of length $x$ , $x+30$ and $x+60.$

Via the Pythagorean Theorem , we have $x^2 + (x+30)^2 = (x+60)^2,$ which simplifies to $x^2 - 60x - 2700 = 0,$ so by the Quadratic Equation or by Factoring Polynomials , we can find $x=-30,90.$ We take the positive solution, so the dimensions of the rectangle are 90 by 120.

Remark: We can avoid some of the Algebra if we note that $x,x+30,x+60$ form an Arithmetic Progression , and the only primitive Pythagorean Triple which has that property is $3,4,5.$ Thus, this triangle has edge lengths that are 30 times a 3-4-5 triangle, so the rectangle dimensions are 90 by 120.

let shortest side =x. Then diagonal x+60, length = x+30 Then by pythagoras theorem.X2 + ( X + 30 )2 = ( X + 60 )2 ; X2 + X2 +60x+900 = X2+120x+3600 ; X2 - 60X - 2700 = 0; (X - 90) (X + 30) - 0, l Then X=90 & X = -30;(not applicable) Therefore Shortest side = 90 & other side = 30