The perimeters of a circle,a square,and an eq | vedclass

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Question

(B) Let the perimeter of each shape be $P$.
For a circle: $2\pi r = P \implies r = \frac{P}{2\pi}$
Area $C = \pi r^2 = \pi \left(\frac{P}{2\pi}\righ

Vedclass · Accepted Answer

$C>S>T$

Vedclass · Answer

(B) Let the perimeter of each shape be $P$. For a circle: $2\pi r = P \implies r = \frac{P}{2\pi}$ Area $C = \pi r^2 = \pi \left(\frac{P}{2\pi}\right)^2 = \frac{P^2}{4\pi} \approx \frac{P^2}{12.56}$ For a square: $4b = P \implies b = \frac{P}{4}$ Area $S = b^2 = \left(\frac{P}{4}\right)^2 = \frac{P^2}{16}$ For an equilateral triangle: $3a = P \implies a = \frac{P}{3}$ Area $T = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} \left(\frac{P}{3}\right)^2 = \frac{\sqrt{3}P^2}{36} \approx \frac{1.732P^2}{36} \approx \frac{P^2}{20.78}$ Comparing the denominators: $12.56 < 16 < 20.78$ Since the numerators are the same, the fraction with the smallest denominator is the largest. Therefore, $C > S > T$.

The perimeters of a circle,a square,and an equilateral triangle are the same,and their areas are $C$,$S$,and $T$ respectively. Which of the following statements is true?

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