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!

Quote:

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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!

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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

Quote:

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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

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

Quote:

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Originally Posted by ThePerfectHacker

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

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than the answer is 57.5cm

Quote:

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Originally Posted by Quick

than the answer is 57.5cm

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Pet peeve warning!! :eek:

ALWAYS convert your units before doing a problem. It leads to fewer mistakes. This one turned out to be correct but don't bet on it in the future.

Pet peeve over. (Whew!) ;)

-Dan