Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A side of an equilateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid points of the sides of the first triangle. The process is continued as shown in the accompanying diagram. Find the perimeter of the sixth i

A side of an equilateral triangle is 20cm long. A second equilateral triangle is inscribed in it by joining the mid points of the sides of the first triangle. The process is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

Answers (1)

Let AB=BC=AC=20cm

Let D, E and F be midpoints of AC, CB and AB which are joined to form an equilateral triangle DEF. So,  CD=CE=10cm. Triangle CDE is equilateral. Hence, DE= 10 cm. Similarly, GH = 5 cm

The series of sides of equilateral triangle will be 20,10,5…..

The series is a G.P with first term 20 and common ratio =1/2

t_{n}=20 \left( \frac{1}{2} \right) ^{n-1}

For the perimeter of 6th triangle we first have to find the side of 6th triangle

t_{6}=\frac{20}{2^{6-1}}=\frac{20}{2^{5}}=\frac{5}{8}cm \\\\

Perimeter would be thrice the length of its side.

    Perimeter of triangle= 3 \left( \frac{5}{8} \right) =\frac{15}{8}cm \\\\

 

 

 

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question