Given:
In isosceles triangle ABC, consider AB=BC and the segment BD with D a point on AC is the median to the base AC.
Perimeter of ABC is 50m and the perimeter of ABD is 40m.
To find:
The length of BD.
Solution:
In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC.
...(i)

...(ii)
Perimeter of ABC is 50m.

[Using (i) and (ii)]


Divide both sides by 2.
...(iii)
Now, perimeter of ABD is 40m.

[Using (iii)]


Therefore, the length of BD is 15m.