CAT 2020 Exam Shift 2 Solved Paper

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