Question 120
Points $P_1$, $P_2$ and $P_3$ are located on the side $AB$ of the triangle $ABC$ so that
$$
|AP_1| = |P_1P_2| = |P_2P_3| = |P_3B| = \frac{1}{4}|AB|.
$$
Parallels with the side $BC$ are drawn through those points and divide the triangle $ABC$ into four parts. The area of the part between the parallels through $P_2$ and $P_3$ equals $5$.
What is the area of the triangle $ABC$? (Purple Comet! Math Meet)
$$
|AP_1| = |P_1P_2| = |P_2P_3| = |P_3B| = \frac{1}{4}|AB|.
$$
Parallels with the side $BC$ are drawn through those points and divide the triangle $ABC$ into four parts. The area of the part between the parallels through $P_2$ and $P_3$ equals $5$.
What is the area of the triangle $ABC$? (Purple Comet! Math Meet)