The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area, $\text{R},$ of the rectangle, both in $\text{sq cm},$ satisfy the relationship $\text{R = T}^{2}.$ If the sides of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is

- $24$
- $27$
- $21$
- $18$