AN is the median of an isosceles triangle ABC with base BC. Find AN if the perimeter of triangle

AN is the median of an isosceles triangle ABC with base BC. Find AN if the perimeter of triangle ABC is 32 cm and the perimeter of ABN is 24 cm.

Decision:

P (ABN) = AB + AN + BN = 24 cm.Then AB + BN = 24 – AN.

Because the triangle is isosceles, then AC = AB, and since AN is the median, then BN = BC. Using this, we get:

P (ABC) = AB + AC + BC = AB + AB + BC = 2AB + BN + NC = 2AB + BN + BN = 2AB + 2BN = 2 (AB + BN) = 2 (24 – AN).

By condition, P (ABC) = 32 cm.We obtain the equation:

2 (24 – AN) = 32;

24 – AN = 32/2;

24 – AN = 16;

AN = 24-16;

AN = 8 cm.

Answer: 8 cm.