Question

Given:

R, S, T are midpoints of , , and .





If the perimeter (distance around) of ABC is 20, then the perimeter of RST is

Answer 1

`10`

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`

`(AR)/(AB)=(1)/(2) \ \ (as\ R\ is\ mid\ point\ of\ AB)`

`(AS)/(AC)=(1)/(2) \ \ (as\ S\ is\ mid\ point\ of\ AC)`

`\angle A=\angle A`

from
`SAS` these two triangles are similar

Hence

`(RS)/(BC)=(AR)/(AB)=(AS)/(AC)=(1)/(2)`

`RS=(BC)/(2)`

Similarly
`RT=(AC)/(2)\ and\ ST=(AB)/(2)`

`Perimeter\ of \ \Delta RST=RS+ST+RT\\\\=(BC)/(2)+(AR)/(2)+(AC)/(2)   \\\\=(AB+AC+BC)/(2)\\\\=(20)/(2)\\\\ =10`