Answer:
Perimeter of ΔDBC = 48 units
Step-by-step explanation:
It's given in he question,
ΔABD ~ ΔDBC
Therefore, by the definition of similar triangles,
Corresponding sides of both the triangle will be proportional.
[tex]\frac{AB}{DB}= \frac{BD}{BC}= \frac{AD}{DC}[/tex]
[tex]\frac{9}{12}= \frac{12}{16}= \frac{AD}{DC}[/tex]
[tex]\frac{3}{4}=\frac{AD}{DC}[/tex]
AD = [tex]\frac{3}{4}DC[/tex] ----------(1)
Since, perimeter of ΔABD = 36,
AB + BD + AD = 36
9 + 12 + AD = 36
AD = 36 - 21
AD = 15
From equation (1),
15 = [tex]\frac{3}{4}(DC)[/tex]
DC = 20
Perimeter of ΔDBC = DB + BC + DC
= 12 + 16 + 20
= 48
Therefore, perimeter of ΔDBC = 48 units is the answer.
