Download App

Sequences and Series — Maths STD 11 Science — Question

CBSE 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→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Evaluate:
$\lim\limits_{\text{x} \rightarrow\frac{\pi}{6}}\frac{\cot^{2}\text{x}-3}{\text{cosec}\text{x}-2}$
→
Solve the following system of equations in R.
$\frac{4}{\text{x}+1}\leq3\leq\frac{6}{\text{x}+1},\text{x}>0$
→
The function f is defined by $\begin{equation} f(x)=\left\{\begin{array}{ll} {1-x,} & {x<0} \\ {1} & {, x=0} \\ {x+1,} & {x>0} \end{array}\right. \end{equation}$
Draw the graph of f(x).
→
If S denotes the sum of an infinite G.P. and $S_1$ denotes the sum of the squares of its terms, then prove that the first terms and common ratio are respectively $\frac{2\text{SS}_1}{\text{S}^2+\text{S}_1}\text{ and }\frac{\text{S}^2-\text{S}_1}{\text{S}^2+\text{S}_1}.$
→
If $a_1, a_2, a_3, ..., an$ are in$ A.P.,$ where $a_i > 0$ for all $i,$ show that:
$\frac{1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_2}}+\frac{1}{\sqrt{\text{a}_2}+\sqrt{\text{a}_3}}+....+\frac{1}{\sqrt{\text{a}_{\text{n}-1}}+\sqrt{\text{a}_\text{n}}}=\frac{\text{n}-1}{\sqrt{\text{a}_1}+\sqrt{\text{a}_\text{n}}}$
→
Out of $25$ members in a family, $12$ like to take tea, $15$ like to take coffee and $7$ like to take coffee and tea both. How many like
$i.$ at least one of the two drinks
$ii.$ only tea but not coffee
$iii.$ only coffee but not tea
$iv.$ neither tea nor coffee
→
Find the sum of n terms of the A.P. whose $k^{th}$ terms is $5k + 1.$
→
Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are $(\text{a} \cos \alpha, \text{a} \sin \alpha)$ and $(\text{a} \cos \beta, \text{a} \sin\beta).$
→
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
→
Find a $G.P.$ for which sum of the first two term is $-4$ and the fifth term is $4$ times the third term.
→