How Do You Calculate the Length of a Crease in a Folded Notecard?

[um0123]

Homework Statement

Take a 3" X 5" notecard and fold it such that point A is on top of point B. Find the length of the crease algebraically.

http://img527.imageshack.us/img527/9913/notecard.jpg

point C is a point created by me.
the dotted line is the crease.
the red line is point A to Point C.

Homework Equations

none

The Attempt at a Solution

i don't even know where to start i have realized that the distance from Point A to Point C(the red line in the diagram) is equal to Point B to Point C. But i don't know how to prove that algebraically, and i don't know how to find the length of the crease.

 

[LCKurtz]

Here's an image of the folded card that might help you:

 

[um0123]

so the length of h would be $$\sqrt{(5-2x)^2 + (3)^2}$$

which equals
$$\sqrt{4x^2-20 x+34}$$

i don't even know how that simplifies.
and how do i find out the correct value of x?

i feel like in not doing the correct thing.

 

[LCKurtz]

Look at the left-most triangle to get an equation you can solve for x.

 

[um0123]

oh, i see. solving that i get x = 1.6

then if i plug it into my equation i got hot h i get $$\sqrt{12.24}$$

but i have one problem, when i plugged 1.6 into that whole equation on of the steps is $$\sqrt{10.24 - 32 + 34}$$

if you add the 32 and 34 together to get 66 before you subtract it from 10.24 you get a negative number under the sqrt, which would mean its imaginery (and we know it can't be). But if you subtract 32 from 10.24 before adding the 34 you get the answer i just posted. This would go agianst the order of operations which states addition goes first. Or is this a case where you just go left to right?

edit: also what is the rule that states that point A to point C, and point B to point C, must be equal?

 

[oNothinGo]

for addition and subtraction, you have to do from left to right. I don't remember there is a rule that states addition goes first. Only know about do multiplication and division first, then addition and subtraction.
or if you want, you can rewrite the equation like this $$\sqrt{10.24-(32-34)}$$.

 

[LCKurtz]

oh, i see. solving that i get x = 1.6

then if i plug it into my equation i got hot h i get $$\sqrt{12.24}$$



edit: also what is the rule that states that point A to point C, and point B to point C, must be equal?

The square root of 12.24 , or approximately 3.498 is correct.

If you look at the picture I drew, the line on top of AC unfolds to give line CB. My picture isn't perfectly to scale.

 

[um0123]

The square root of 12.24 , or approximately 3.498 is correct.

If you look at the picture I drew, the line on top of AC unfolds to give line CB. My picture isn't perfectly to scale.

i see that, but i was wondering if there is a proof rule that i can state. or is it just assumed?

 

[LCKurtz]

i see that, but i was wondering if there is a proof rule that i can state. or is it just assumed?

If you label the lower right corner of the original rectangle D and the lowest point on the dotted line triangle at the bottom E, triangles ACE and CBD are congruent:

AE = BD = 3, (they are the same edge of the paper)

CE = CD = x (they are also the same edge)

and the included right angle. AC and BC are the equal hypotenuses.