In isosceles triangle ABC the segment BD with D a point on AC is the median to the base AC. Find BD if the perimeter of ABC is 50m and the perimeter of ABD is 40m

Answers

Answer 1

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.


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