Question

The perimeter of a circle, square and an equilateral triangle are equal. Which one of the following statement is true?

• A.
  The circle has the largest area
• B.
  The square has the largest area
• C.
  The equilateral triangle has the largest area
• D.
  All the three shapes have same area

Answer 1

The correct option is A

The circle has the largest area
$P_C=P_S=P_T$

$\pi D=4a=3s$

$Now,Areaofcircle$

$=\frac{\pi }{4}{D}^2[\pi D=4a]$

$Areaofsquare=a^2$

$=\frac{{\pi }^2{D}^2}{16}=\frac{{\pi }^2}{16}{D}^2$

$Areaoftriangle$

$=\frac{\sqrt{3}}{4}{s}^2=\frac{\sqrt{3}}{4}{\left(\frac{\pi D}{3}\right)}^2$

$\{\because \pi D=3s\}$

$=\frac{\left(\sqrt{3}\right){\pi }^2{D}^2}{36}$

$\because \frac{\pi }{4}>\frac{{\pi }^2}{16}>\frac{\sqrt{3}{\pi }^2}{36}$

$So,circlehasthelargestarea.$