Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A wire of length is to be cut into two pieces. One of the pieces is to be made into a squ

A wire of length 22 \mathrm{~m} is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

Option: 1

\frac{22}{9+4 \sqrt{3}}


Option: 2

\frac{66}{9+4 \sqrt{3}}


Option: 3

\frac{22}{4+9 \sqrt{3}}


Option: 4

\frac{66}{4+9 \sqrt{3}}


Answers (1)

best_answer

Let the side of square be \mathrm{x} and side of triangle be \mathrm{z}

So  \mathrm{4 x+3 z=22} \\

\mathrm{\Rightarrow x=\frac{22-3 z}{4}}          ..........(i)

\text { combined area } \mathrm{A =x^{2}+\frac{\sqrt{3}}{4} z^{2}} \\

\mathrm{= \frac{1}{16}(22-3 z)^{2}+\frac{\sqrt{3}}{4} z^{2} }

\mathrm{\frac{d A}{d z}=0\: for\: max/min\: area}\\

\mathrm{\Rightarrow-\frac{3}{8}(22-3 z) +\frac{\sqrt{3}}{2} z=0} \\

\mathrm{\Rightarrow \quad \frac{\sqrt{3}}{2} z=\frac{3}{8}(22-3 z) }\\

\mathrm{\Rightarrow \quad 4 z=22 \sqrt{3}-3 \sqrt{3} z} \\

\mathrm{\Rightarrow \quad z=\frac{22 \sqrt{3}}{4+3 \sqrt{3}}=\frac{66}{4 \sqrt{3}+9} }

Hence the correct answer is option 2

Posted by

Pankaj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: BTech CSE cut-offs for PwD candidates at NITs make entry easy; top institutes still selective
anam-khan

73 or 99 percentile? JEE Main result questioned, J-K candidate says, ‘Don’t create hype’
anam-khan

JEE Main 2025: 11 from Kota coaching centres among 24 students with 100 percentile

Latest Question