Question : A piece of wire 132 cm long is bent successively in the shapes of an equilateral triangle, a square, and a circle. The area will be largest in the shape of:
Option 1: Circle
Option 2: Equilateral triangle
Option 3: Square
Option 4: Equal in all the shapes
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: Circle
Solution :
The length of the wire is the same in all three cases, so it becomes the perimeter of each shape.
(1). For an equilateral triangle with side length $a$, the perimeter = $3a$
$a = \frac{132}{3} = 44$ cm
The area of an equilateral triangle $ = \frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4}(44)^2= 838.32$ cm
2
(2). For a square with side length $a$, the perimeter = $4a$. So, $a = \frac{132}{4} = 33$ cm
The area of a square $ = a^2 = (33)^2= 1089$ cm
2
(3). For a circle with radius $r$, the circumference = $2\pi r$
$2\pi r=132$
⇒ $r = \frac{132}{2\pi} $
The area of a circle $ = \pi r^2 = \pi \left(\frac{132}{2\pi}\right)^2= 1386$ cm
2
The area will be largest in the shape of a circle.
Hence, the correct answer is 'Circle'.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
