Question

Given the regular octagon, what is the length of any side?

Answer 1

Answer:110

Step-by-step explanation:x^2+17x=15x+35

x^2+17x-15x-35=0

x^2+2x-35=0

delta=2^2-4*1*(-35)=4+140=144

x1=(-2+V144)/2=(-2+12)/2=10/2

x=5

so 15*5+35=75+35=110

Answer 2

110

Explanation:

In a regular polygon, each side has the same length.

Therefore we have the equation:

`x^2+17x=15x+35`

We must specify the domain:

`x^2+17x>0\ \wedge\ 15x+35>0\\\\x(x+17)>0\ \wedge\ 15x>-35\\\\(x<-17\ \vee\ x>0)\ \wedge\ x>-(7)/(3)\Rightarrow x>0`

`x^2+17x=15x+35\qquad\text{subtract}\ 15x\ \text{from both sides}\\\\x^2+17x-15x=15x-15x+35\\\\x^2+2x=35\qquad\text{add 1 to both sides}\\\\x^2+2x+1=35+1\\\\x^2+2(x)(1)+1^2=36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=36\to x+1=\pm√(36)\\\\x+1=\pm6\qquad\text{subtract 1 from both sides}\\\\x+1-1=\pm6-1\\\\x=-7\ \vee\ x=5`

`x<-7\\otin\text{domain};\ x=5\in\text{domain}`

The length of a side:

`x^2+17x=5^2+17(5)=25+85=110\\\\15x+35=15(5)+35=75+35=110`