Discussion Forum

An equilateral triangle, a square and a circle have equal perimeters. If $T$, denotes the area of the triangle, $S$, the area of the square and $C$, the area of the circle, then :

Answer:

Explanation:

Let the perimeter of each be $a$.

Then, side of the equilateral triangle $=\frac{a}{3}$: side of the square $=\frac{a}{4}$;

Radius of the circle $=\frac{a}{2\pi}$.

$\therefore T$ $=\frac{\sqrt{3}}{4}$ $\times\left(\frac{a}{3}\right)^{2}$

$=\frac{\sqrt{3}a^{2}}{36}$; $S=\left(\frac{a}{4}\right)^{2}$

$=\frac{a^{2}}{16}$; $C$ $=\pi\times\left(\frac{a}{2\pi}\right)^{2}$ $=\frac{a^{2}}{4\pi}$

$=\frac{7a^{2}}{88}$.

So, $C>S>T$.