Posted by **Kelsey** on Saturday, October 29, 2011 at 5:41pm.

A rectangular sheet of paper of width a and length b, where 0<a<b, is folded by taking one corner of the sheet and placing it at point P on the opposite long side of the sheet. The fold is flatened to form a crease across the sheet. Assuming that the fold is made that there is no flap extending beyond the original sheet, find the point P that produces the crease of minimum length. What is the length of that crease?

- math (calculus) -
**Steve**, Monday, October 31, 2011 at 12:14am
If we label the lower left corner A, and go clockwise for B,C,D

then with some actual folding experimentation, we see that P can go along side BC at a distance x from B, which can vary from b-sqrt(b^2-a^2) to a. Anywhere else the fold produces a flap that extends beyond the sheet.

When x = b-sqrt(b^2-a^2) the fold length is just the long side of the rectangle, b. That is, P is a distance sqrt(b^2-a^2) from C.

When x = a, the fold length is just the diagonal of a square, a√2

It's late. I'll let you figure out in which cases one is greater than the other.

## Answer this Question

## Related Questions

- maths - what is the volume of box if volume of cylinder is 48.125 cubic cm, ...
- maths-urgently needed - The volume of a cylinder is 48.125 cm3, which is formed ...
- math - A rectangular sheet of metal, of area 440 sq.cm is folded into a cylinder...
- maths --plse help me.. - THE VOLUME OF A CYLINDER IS 48.125cm cube , WHICH IS ...
- maths - how cards of side 5cm can you cut from a rectangular sheet of paper of ...
- maths - how many square cards of side 5cm can you cut from a rectangular sheet ...
- Math - A box with an open top is to be constructed by cutting a-inch squares ...
- volume - hi, um im not sure how to do this.So can you please help me? coral ...
- Math - From an 8 inch by 10 inch rectangular sheet of paper, squares of equal ...
- math - Sarah is making poster by hand to advertise her school play, but her ...

More Related Questions