Question

Given:

Answer 1

Answer:

$10$

Step-by-step explanation:

Given that $R,S,T$ are mid points of the sides of the triangle $ABC$

Perimeter of $\Delta ABC=AB+AC+BC=20$

In the $\Delta ARS\ and\ \Delta ABC$

$\frac{AR}{AB}=\frac{1}{2} \ \ (as\ R\ is\ mid\ point\ of\ AB)$

$\frac{AS}{AC}=\frac{1}{2} \ \ (as\ S\ is\ mid\ point\ of\ AC)$

$\angle A=\angle A$

from $SAS$ these two triangles are similar

Hence

$\frac{RS}{BC}=\frac{AR}{AB}=\frac{AS}{AC}=\frac{1}{2}$

$RS=\frac{BC}{2}$

Similarly $RT=\frac{AC}{2}\ and\ ST=\frac{AB}{2}$

$Perimeter\ of \ \Delta RST=RS+ST+RT\\\\=\frac{BC}{2}+\frac{AR}{2}+\frac{AC}{2} \\\\=\frac{AB+AC+BC}{2}\\\\=\frac{20}{2}\\\\ =10$