1. ## Help! Octagon

The longest diagonal of a rectangular octagon varies directly as the length of a side. if a regular octagon with sides 6mm has a diagonal of lenth 23mm, how long is the diagonal of an octagon with side of 15cm?

Is there a formula for this? I dont know where to start. thanks!

2. Originally Posted by sallyann
The longest diagonal of a rectangular octagon varies directly as the length of a side. if a regular octagon with sides 6mm has a diagonal of lenth 23mm, how long is the diagonal of an octagon with side of 15cm?

Is there a formula for this? I dont know where to start. thanks!
notice I highlighted "directly"

this means that as the length of a side increases, the diagonal of the octagon increases at a constant amount as well.

Think of a line: y=mx

where y is the diagonal, and x is the side.

thus: y/x=m

now substitute known values: 23/6=m

now that gives equation: y=(23/6)x

now substitute 15 for side length: y=(23/6)(15)=57.5

so the diagonal is 57.5

3. Originally Posted by Quick
notice I highlighted "directly"

this means that as the length of a side increases, the diagonal of the octagon increases at a constant amount as well.

Think of a line: y=mx

where y is the diagonal, and x is the side.

thus: y/x=m

now substitute known values: 23/6=m

now that gives equation: y=(23/6)x

now substitute 15 for side length: y=(23/6)(15)=57.5

so the diagonal is 57.5
I am no engineer but one is in millemeters and the other in centimenters!

4. Originally Posted by ThePerfectHacker
I am no engineer but one is in millemeters and the other in centimenters!