Twisted Triangle

Given that $\triangle ABC$ is equilateral with side 1 unit, $AP=BR=CQ=\dfrac 15$ and perimeter of the colored triangle is $a \times \sqrt{\dfrac {a}{b}}$ , find $a+b$ , where $a$ and $b$ are relatively prime.

"The general problem of finding perimeter of colored triangle when $AP=BR=CQ=m;m<1$ appeared in the Chennai Mathematical Institute Undergraduate Entrance Exam 2018"