Answer:
[tex]10[/tex]
Step-by-step explanation:
Given that [tex]R,S,T[/tex] are mid points of the sides of the triangle [tex]ABC[/tex]
Perimeter of [tex]\Delta ABC=AB+AC+BC=20[/tex]
In the [tex]\Delta ARS\ and\ \Delta ABC[/tex]
[tex]\frac{AR}{AB}=\frac{1}{2} \ \ (as\ R\ is\ mid\ point\ of\ AB)[/tex]
[tex]\frac{AS}{AC}=\frac{1}{2} \ \ (as\ S\ is\ mid\ point\ of\ AC)[/tex]
[tex]\angle A=\angle A[/tex]
from [tex]SAS[/tex] these two triangles are similar
Hence
[tex]\frac{RS}{BC}=\frac{AR}{AB}=\frac{AS}{AC}=\frac{1}{2}[/tex]
[tex]RS=\frac{BC}{2}[/tex]
Similarly [tex]RT=\frac{AC}{2}\ and\ ST=\frac{AB}{2}[/tex]
[tex]Perimeter\ of \ \Delta RST=RS+ST+RT\\\\=\frac{BC}{2}+\frac{AR}{2}+\frac{AC}{2} \\\\=\frac{AB+AC+BC}{2}\\\\=\frac{20}{2}\\\\ =10[/tex]
