Triangle ABC is isosceles, AC is the base of the triangle. The perimeter of triangle ABC is 13 cm

Triangle ABC is isosceles, AC is the base of the triangle. The perimeter of triangle ABC is 13 cm and the perimeter of triangle DBC is 10.5 cm.Find the median BD

Given:

isosceles triangle ABC,

the base of the speaker,

P ABC = 13 centimeters,

BD – median,

P DBC = 10.5 centimeters.

Find the length of the median BD -?

Solution:

1. Consider an isosceles triangle ABC. The median BD is the height.

2. Right-angled triangle ABD = right-angled triangle BDC along two legs.

3. P ABC = AB + BC + AD = P BDC + P ABD – 2 * BD;

(P BDC + P ABD) – P ABC = 2 * BD;

BD = ((P BDC + P ABD) – P ABC): 2;

BD = ((10.5 + 10.5) – 13): 2;

BD = (21 – 13): 2;

BD = 8: 2;

BD = 4 centimeters.

Answer: 4 centimeters.