Download App

Sequences and Series — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSequences and Series3 Marks
Question
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. This process is continued for third, fourth, fifth, triangles. Find the perimeter of the sixth inscribed equilateral triangle.
✓

Answer

Let the given equilateral triangle be $\triangle\text{ABC}$ with each side of 20cm.
By joining the mid-points of this triangle, we get another equilateral triangle of side equal to half of the length of side of $\triangle\text{ABC.}$
Continuing in this way, we get a set of equilateral triangles with side equal to half of the side of the previous triangle.
Now,
Perimeter of first triangle = 20 × 3 = 60cm;
Perimeter of second triangle = 10 × 3 = 30cm;
Perimeter of third triangle = 5 × 3 = 15cm;
Clearly 60, 30, 15 ...., from a G.P. with a = 60 and $\text{r}=\frac{30}{60}=\frac{1}{2}.$
We have, tofind perimeter of sixth incribed triangle i.e., we have to fiind the sixth term of the G.P.
$\therefore$ Perimeter of sixth incribed triangle
$\text{a}_6=\text{ar}^{6-1}=60\times\Big(\frac{1}{2}\Big)^5=\frac{60}{32}=\frac{15}{8}\text{cm}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Sequences and Series→Sequences and Series — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$
  1. $6$
  2. $1$
  3. $\frac16$
  4. None of these
→
Find the domain and range of the following real valued functions:
f(x) = |x - 1|
→
Find the centroid of a triangle, mid-points of whose sides are (1, 2, -3), (3, 0, 1) and (-1, 1, -4).
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}(\cos\text{x}+\sin\text{x})^{\frac{1}{\text{x}}}$
→
If ${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$. find r .
→
Solve: ${x^2} - 2x + \frac{3}{2} = 0$
→
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b $ \in $A, b is exactly divisible by a}.
  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.
→
Let sum of n, 2n, 3n  terms of an A.P. be S1, S2 and S3 respectively, show that S3 = 3(S2 - S1).
→
Find the sum of the following geometric progrssions:

$4,2,1,\frac{1}{2}\ ...\text{to 10 terms.}$ 

→
If $\tan69^\circ+\tan66^\circ-\tan69^\circ\tan66^\circ=2\text{k},$ then k =
  1. $-1$
  2. $\frac12$
  3. $\frac{-1}{2}$
  4. none of these
→