# Conversion of Algebra To Geometry is an art

Geometry Level 5

Let $a,b \in R$ such that $E$ is minimum where $E=\sqrt { { a }^{ 2 }+{ b }^{ 2 } } +\sqrt { { (a-12) }^{ 2 }+{ b }^{ 2 } } +\sqrt { { a }^{ 2 }+{ (b-5) }^{ 2 } }$ Let ${ E }_{ \text{min} }^{ 2 }=m+n\sqrt { l }$ where $m,n$ are co-prime integers and $l$ is a square free integer. Then, find the value of $m+n+l$.

###### Hint:

Don't Use Calculus since here it is Poisonous for you.