Let $ABC$ be triangle with sides that are not equal. Find point $X$ on $BC$ From following conditions. Let $ABC$ be triangle with sides that are not equal. Find point $X$ on $BC$ such that $$\frac{\text{area}\ \triangle{ABX}}{\text{area}\ \triangle{ACX}}=\frac{\text{perimeter}{\ \triangle{ABX}}}{\text{perimeter}{\ \triangle {ACX}}}$$
I am not getting how to start with, Clearly  $ABC$ triangle is scalene but what about other triangle is it necessary they should be scalene too? Please help me to solve this. Thanks in advance

Hint: It makes sense to rewrite this as
$$\frac{\text{area}\ \triangle{ABX}}{\text{perimeter}{\ \triangle{ABX}}}=\frac{\text{area}\ \triangle{ACX}}{\text{perimeter}{\ \triangle {ACX}}},$$
since that way each side depends only on one triangle. Now, what do you know about the ratio of area to perimeter? Does it equal any other quantity in a triangle that you know about?
