Problema Solution
A rectangular sheet of paper measures 12" by 9". One corner is folded onto the diagonally opposite corner and the paper is creased. What is the length in inches of the crease? Give 3 solutions.
Answer provided by our tutors
We choose one solution. If a rectangular sheet of paper is folded diagonally against the opposite corner in such a way that the 9" sheet is unexposed, then let 'x' represent the length of the 12" sheet which has been pressed against the sheet of paper. The remainder of the unexposed portion would be "12-x".
The folding defines an unexposed right triangle whose base is '12-x', its leg is 9" and the hypotenuse is 'x'. We solve for 'x' in order to know how long of the sheet has been folded over:
x^2=9^2+(12-x)^2
x=75/8
The angle exposed in such a fold is approximately 73.73 [asin(9/(75/8))].
The folded area of the sheet then defines a right triangle who hypotenuse is 'x', whose angle is approximately:
((180-73.73)/2)
53.135
This defines a right triangle whose hypotenuse is 'x', whose angle is approximately 53.135 and we solve for the base, which is then approximately 5.62.
The final length of the crease would be 2*5.62 = 11.24
So one such crease would be approximately 11.24".