Question

An artist has been commissioned to make a stained glass window Please check photo

Answer 1

7.46

Step-by-step explanation:

To find the side of the octagon, we will use the triangles on the corner.

The legs of these triangles are (18 - x)/2 and the hypotenuse is x. So, using the Pythagorean theorem, we can write the following equation

`x^2=((18-x)/(2))^2+((18-x)/(2))^2`

Then, we need to rewrite this expression

`\begin{gathered} x^2=2((18-x)/(2))^2 \\ \\ x^2=(2(18-x)^2)/(2^2) \\ \\ x^2=(2(18-x)^2)/(4) \\ \\ x^2=((18-x)^2)/(2) \\ \\ 2x^2=(18-x)^2 \\ 2x^2=18^2-2(18)(x)+x^2 \\ 2x^2=324-36x+x^2 \\ 2x^2-324+36x-x^2=0 \\ x^2+36x-324=0 \end{gathered}`

Using the quadratic equation, we get that the solution is

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ \text{ Where a = 1, b = 36, and c = -324. Then} \\ \\ x=(-36\pm√(36^2-4(1)(-324)))/(2(1)) \\ \\ x=(-36\pm√(2592))/(2) \\ \\ x=(-36\pm50.91)/(2) \\ \\ \text{ Therefore} \\ x=(-36+50.91)/(2)=7.46 \\ or \\ x=(-36-50.91)/(2)=-43.46 \end{gathered}`

x = -43.46 doesn't have sense here, so the length of each side of the octagon is 7.46