Answer:
17.25 cm
Step-by-step explanation:
We are given that
Perimeter of triangle ABC=27.6 cm
AB=9.6 cm
BC=6 cm
Triangle ABC is similar to triangle BCD
We have to find the perimeter of triangle BCD.
Triangle ABC is similar to triangle BCD
Let perimeter of triangle BCD=x
When two triangles are similar then
[tex]\frac{Perimeter\;of\;triangle}{Perimeter\;of\;another\;triangle}=\frac{Side\;of\;triangle}{side\;of\;another\;triangle}[/tex]
Using the formula
[tex]\frac{perimeter\;of\;triangle\;ABC}{perimeter\;of\;triangle BCD}=\frac{AB}{BC}[/tex]
Substitute the values
[tex]\frac{27.6}{x}=\frac{9.6}{6}[/tex]
[tex]x=\frac{27.6\times 6}{9.6}=17.25 cm[/tex]
Hence, the perimeter of triangle BCD=17.25 cm
