Beer soaked ramblings follow.
Yes, thou art correct.
Another approach I see is to divide the square in the middle and connect the bottom midpoint with either the left or the right upper corner. Apply the pythagorean theorem to solve the length of the left or right diagonal (which is equal to the radius of the half circle) and you're done.
It's correct, but unnecessarily complex. I used the pythagorean theorem approach mentioned above.Here it is..
It's correct, but unnecessarily complex. I used the pythagorean theorem approach mentioned above.
Easier still: straight line from center of circle to an upper corner = radius,
and creates ye olde 30-60-90 triangle with sides 3,6,r ....
I wonder why i went down such a complicated route? Why is it that some people can just spot the simple way in while others ( like me) look for complications!
I would imagine the figure made you think of one you've seen before, so you took the route associated with that other problem. The more problems you've seen, the more possibilities you have to notice.
A good habit, also, is after solving a problem to look back at it and see what other methods you can find (sometimes inspired by something about the answer, such as its simplicity). If you do that enough, you will develop an ability to see alternative methods for new problems, too.
Can anyone offer me hints or check the answer i have got?
I got sqrt(45) using a mixture of theorem involving semi-circles and similar triangles.
But i would be interested..
1) if i am correct?
2) Any other approaches?