A side of an equilarteral triangle is 20 cm long .A second equilateral triangle is inscribed in it by joning the mid -point of the sides of the first triangle . The process is caontinued as shown in the accompanying diagram . find the perimeter of the sixth inscribed equilateral triangle .

Explanation

Side of equilateral `Delta ABC` = 20 cm By joining the mid -points if this triangle , we get another equilateral triangle of side equal to half of the length of side of `Delta ABC`
continuing in this way , we get a set of equilateral triangles with side equal to half of the side of the previous triangle .
`therefore ` Perimeter of first triangle `=20xx3=60cm`
perimeter of second triangle `=10xx3=30cm`
perimeter of third triangle `=5xx3=15 cm`
Now , the seires will be 60,30,5 ... Here a=60
`therefore r=(30)/(60)=(1)/(2) [ :' ("second terms")/("first term")=r]`
we have to find perimeter of skin inscribed triangle it is the skin it is the sixth term t' e. series.
` therefore a_(6)=ar^(6-1) [ :' a_(n)=ar^(n-1)]`
` =60xx((1)/(2))^(5)=(60)/(32) =(15)/(8) cm `