The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?
draw the top part of the cut-off
let each side of the octagon be x m
let the amount that has to be cut off be y
I see a right-angled triangle with hypotenuse x and the other 2 sides are y
x^2 = y^2 + y^2
x^2 = 2y^2
x = 2√y or y = x/√2
now along the top of the original square:
y + x + y = 2
x/√2 + x + x/√2 = 2
times √2
x + √2x + x = 2√2
x(√2+2) = 2√2
x = 2√2/(√2+2)
rationalizing:
x= 2√2/(√2+2) * (√2-2)/(√2-2)
= 2√2 - 2 or appr 0.8284
I just noticed that you posted this same question 9 times !
and it had already been answered.
Very annoying.
Don't you check back to see if somebody answered your earlier question??
i didn't know i posted it 9 times. i always check back the page if my question is answered. hahaha. i keep on refreshing it. lol. THANK YOU SO MUCH!!
Hmmm. A good lesson. We have been attributing to malice what was done in ignorance.
So, Lian, once the question is posted, go back to the main list, and click in your link. Then you can refresh the page without reposting the question.
To find the length of the side of the resulting octagon, we can start by calculating the length of one of the sides of the original square.
Given that the square has sides of 2 meters, each side of the square is 2 meters long.
Next, we need to determine the length of the sides that are cut off to form the octagon. Since the corners of the square are removed equally, we can conclude that each side of the octagon is formed by cutting off an equal length from each corner of the square.
To calculate the length of the side that is cut off, we can divide the length of one side of the square by 2, because we are cutting each corner in half.
So, (2 meters) / 2 = 1 meter. Therefore, the length of each side that is cut off to form the octagon is 1 meter.
Now, to find the length of one side of the resulting octagon, we subtract the length of the side that is cut off from the original side length.
(2 meters) - (1 meter) = 1 meter.
Therefore, the length of one side of the resulting octagon is 1 meter.