Question

An artist has been commissioned to make a stained glass window in the shape of a regular octagon. The octagon must fit inside a 28 in square space. Determine the length of each side of the octagon. Round to the nearest hundredth of an inch. 28 in

Answer 1

We have the next equation

$28=x+\frac{x}{\sqrt[]{2}}+\frac{x}{\sqrt[]{2}}$

we factorize the x

$28=x(1+\frac{2}{\sqrt[]{2}})$

we isolate the x

$x=\frac{28}{1+\frac{2}{\sqrt[]{2}}}=11.60$

The side of the octagon is 11.60 in