MathDB

Let

ABC

be a triangle with

BC = 5

CA = 3

, and

AB = 4

. Variable points

P, Q

are on segments

AB

AC

, respectively such that the area of

APQ

is half of the area of

ABC

. Let

x

and

y

be the lengths of perpendiculars drawn from the midpoint of

PQ

to sides

AB

and

AC

, respectively. Find the range of values of

2y + 3x

Problem Statement