UPSC CDS 1 2022 Math Paper

Given:
AD is the bisector of ∠BAC
AB=12cm,BD=10cm,DC=5cm
Concept used:
Angle bisector theorem: The angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two-line segments is proportional to the ratio of the other two sides.
Perimeter = Sum of the three sides
Calculation: According to the concept,
In △ABC ,
AB∕AC=BD∕DC
⇒12∕AC=10∕5
⇒60=10AC
⇒60∕10=AC
⇒AC=6cm
Now, Perimeter of △ABC=AB+BC+AC
⇒ Perimeter of ∆ABC=12+15+6[∵BC=BD+DC]
⇒ Perimeter of △ABC=33
∴ The perimeter of the triangle is 33cm