Find-the-perimeter-of-a-regular-heptagon-ABCDEFG-if-1-AE-1-AC-1-5-

Question Number 183747 by HeferH last updated on 29/Dec/22

F i n d t h e p e r i m e t e r o f a r e g u l a r h e p t a g o n

A B C D E F G i f \frac{1}{A E} + \frac{1}{A C} = \frac{1}{5}

Answered by mr W last updated on 29/Dec/22

θ = \frac{5 π}{7}

A E = 2 a \sin \frac{θ}{2} = 2 a \sin \frac{5 π}{14}

A E = a + 2 a \sin (θ - \frac{π}{2}) = a (1 + 2 \sin \frac{3 π}{14})

\frac{1}{2 a \sin \frac{5 π}{14}} + \frac{1}{a (1 + 2 \sin \frac{3 π}{14})} = \frac{1}{5}

\frac{a}{5} = \frac{1}{2 \sin \frac{5 π}{14}} + \frac{1}{1 + 2 \sin \frac{3 π}{14}} = 1

\Rightarrow a = 5

P = 7 a = 35

Commented by HeferH last updated on 29/Dec/22

t h a n k s :)

Facebook Tweet Pin