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.
[tex]AB=BC[/tex] ...(i)
[tex]AD=CD[/tex]
[tex]AC=2AD[/tex] ...(ii)
Perimeter of ABC is 50m.
[tex]AB+BC+AC=50[/tex]
[tex]AB+AB+2AD=50[/tex] [Using (i) and (ii)]
[tex]2AB+2AD=50[/tex]
[tex]2(AB+AD)=50[/tex]
Divide both sides by 2.
[tex]AB+AD=25[/tex] ...(iii)
Now, perimeter of ABD is 40m.
[tex]AB+AD+BD=40[/tex]
[tex]25+BD=40[/tex] [Using (iii)]
[tex]BD=40-25[/tex]
[tex]BD=15[/tex]
Therefore, the length of BD is 15m.
