Same post answered by Steve
http://www.jiskha.com/display.cgi?id=1467634318
Two identical circles are to be cut from
a 12cm by 9cm sheet of paper.
What is the maximum possible radius of these circles?
Show that if the length of the sheet of paper is twice the breadth of the paper, then the radius of the largest circles which can be cut out is half of the breadth.
Considering Pythagoras to the right angle
3 answers
Apply Pythagoras to the right angle with
sides 2r, 12-2r and 9-2r.
This leads to the equation
4r2 – 85r + 225 =0
which solves to give r = 3.15
In the case where breadth is ‘b’ and the length is 2b, form the right angled triangle with sides
2r, 2b-2r and b-2r and proceed using the quadratic formula to get the solutions
r=5b/2 , b/2
The first solution is rejected.
how do you explain this? thanks in advanced
sides 2r, 12-2r and 9-2r.
This leads to the equation
4r2 – 85r + 225 =0
which solves to give r = 3.15
In the case where breadth is ‘b’ and the length is 2b, form the right angled triangle with sides
2r, 2b-2r and b-2r and proceed using the quadratic formula to get the solutions
r=5b/2 , b/2
The first solution is rejected.
how do you explain this? thanks in advanced
Hmmm. I originally rejected the idea that the centers would lie on the diagonal, because I thought the circles would overlap or not fill the maximum area.
I'm not sure how your equation comes about, but it appears you have solved the problem.
I'm not sure how your equation comes about, but it appears you have solved the problem.