Between-a-square-a-triangle-and-a-circle-of-the-same-perimeter-which-shape-has-the-least-area-

Question Number 110781 by Aina Samuel Temidayo last updated on 30/Aug/20

Between a square, a triangle and a

circle of the same perimeter, which

shape has the least area ?

Commented by mr W last updated on 30/Aug/20

t r i a n g l e < s q u a r e < c i r c l e

Commented by Aina Samuel Temidayo last updated on 30/Aug/20

Solution please ?

Answered by $@y@m last updated on 30/Aug/20

L e t c o m m o n p e r i m e t e r = 12 x

A r e a o f s q u a r e = {(3 x)}^{2} = 9 x^{2} \dots . (1)

A r e a o f t r i a n g l e = \frac{\sqrt{3}}{4} {(4 x)}^{2} = 4 \sqrt{3} x^{2} \approx 6.93 x^{2} \dots (2)

A r e a o f c i r c l e = π {(\frac{12 x}{2 π})}^{2} \approx 11.45 x^{2} \dots (3)

(3) > (1) > (2)

Commented by Aina Samuel Temidayo last updated on 30/Aug/20

Thanks .