Question

AM is the median of BC, a line through M intersects AB at median P, area of APM is 35, find the area of APC and the area of PMC.

A) Area of APC = 70, Area of PMC = 70
B) Area of APC = 35, Area of PMC = 35
C) Area of APC = 105, Area of PMC = 35
D) Area of APC = 35, Area of PMC = 17.5

Answer 1

The area of triangle APC is 35, and the area of triangle PMC is 17.5, as APC and APM share the same base and height, and PMC has half the base of APM. The correct answer is option D).

Step-by-step explanation:

The problem requires us to find the area of triangles APC and PMC, given that AM is the median of BC, a line through M intersects AB at median P, and the area of triangle APM is 35. Since AM is the median, it divides triangle ABC into two triangles of equal area.

Also, since P is the median to AB, triangles APM and APC have equal areas because they have the same base and height. Therefore, the area of triangle APC is also 35.

For triangle PMC, it shares the same height with triangle APM but has half the base length because M is the midpoint of BC, which makes its area half of APM, so the area of PMC is 17.5.