The perimeter of an isosceles triangle ABC (AB = BC) is 16 cm. The perimeter of the triangle ABM, where M

The perimeter of an isosceles triangle ABC (AB = BC) is 16 cm. The perimeter of the triangle ABM, where M is the middle of the segment AC, is 12 cm. Find the length of the median BM.

It is known from the condition that P (ABC, where AB = BC)) = 16 cm. It is also known that the perimeter of the triangle ABM, where M is the midpoint of the segment AC, is 12 cm.

Let’s calculate the length of the median of the VM.

Draw triangle ABC and draw median BM.

The median divides the opposite side in half, as defined.

AB = BC = a, then we write the perimeter:

P (ABC) = a + a + AC;

16 = 2a + AM + MC;

AM = MC (the median divides the side into two equal parts).

2a + 2AM = 16;

a + AM = 8;

AM = 8 – a;

P (ABM) = AB + BM + AM;

12 = a + BM + 8 – a;

BM + 8 = 12;

BM = 4.

Answer: 4.