IIITH-PGEE 2017

Question

For same perimeter $p$ which of these will have least area:

A. Rectangle

B.Equilateral triangle

C.Right triangle

D.Circle

E. Regular hexagon

Answer 1

C. Right triangle

Comments

Oh Yes. :)

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for same perimeter p,  Area will be in the following order-

circle > hexagon > square > rectangle > equilateral triangle > right triangle

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Could u explain how it is ?

Answer 2

Rectangle area = width * length         Perimeter of the rectangle = 2(l + b)

Equilateral triangle =  3^1/2 / 4              Perimeter of Equilateral triangle = 3a

Right triangle = 1/2 *ab                        Perimeter of Right Triangle = a+b+(a²+b²)^1/2

Circle = pi*r*r                                        Perimeter of circle = 2*pi*r

Regular Hexagon=  3* 3² / 2  * a²           Perimeter of hexagon = 6a

Order for same perimeter p,  Area will be in the following order-         

 circle > hexagon > square > rectangle > equilateral triangle > right triangle

hence,  For same perimeter pp which of these will have least area  = right triangle                       ans: C