I swear to Cecil I have not been in school for 8 years, so this isn’t a homework question, I just have a personal little project that I’m too dumb for.
How do you figure out the measurement for the side of a square if you know the measurement for the diagonal?
(The square’s gotta fit inside a circle, the points at the corners of the square rest on the circle, so I figure the diagonal of the square is equal to the diameter of the circle- right?)
It’s the square root of two times the radius of the circle.
When you have a square divided by a diagonal, you have two equilateral right triangles.
Remember the Pythagorean Theorem? a[sup]2[/sup] + b[sup]2[/sup] = c[sup]2[/sup].
In this case, a=b, and you know c (the length of the diagonal). So,
2a[sup]2[/sup] = c[sup]2[/sup], where a=the length of the side, and c=the length of the diagonal.
Oops.
Don’t know what a circle has to do with it. Side = diagonal/(square root of 2), in case you can’t solve the equation in the prior post.
O.K. so
the diameter of the circle / diagonal of the square is 4.75"
squared is: 22.5625"
half of which is equal to a[sup]2[/sup], right? So a[sup]2[/sup] is 11.28125"
and then a = 3.358757yadda yadda yadda (for my purposes 3 1/3 is o.k.)
Am I correct?
Actually, you’re correct (as are the others). According to Smeghead (correctly), 2a[sup]2[/sup]=c[sup]2[/sup] (a=side of square, c=diameter of circle). So a=c / sqrt(2). Since c=2r (r=radius), a=2r / sqrt(2) = sqrt(2)r, which was your answer.
Yep.
Thanks, all!