Thread: A rectangle

I have a rectangular piece of paper (ABCD), with a width of 3 and a length of 4. I fold it diagonally so that vertex A touches vertex C. What is the length of the crease in the paper?

I have a drawing, containing all that I know so far (its not to scale). The red line is what I am supposed to find out. Also, I do not want to use any trigonometry functions, such as arctan, tan, sin etc.

Thanks.

Originally Posted by Grey

I have a rectangular piece of paper (ABCD), with a width of 3 and a length of 4. I fold it diagonally so that vertex A touches vertex C. What is the length of the crease in the paper?

I have a drawing, containing all that I know so far (its not to scale). The red line is what I am supposed to find out. Also, I do not want to use any trigonometry functions, such as arctan, tan, sin etc.

Thanks.

Call the point of intersection of the red line and the side AD point E. Call the center of the rectangle (the point of intersection of the red line and the diagonal AC) the point F.

Here's a hint. Notice that triangle AFE is similar to triangle ADC. (I leave this proof to you.)

-Dan

Originally Posted by Grey

I have a rectangular piece of paper (ABCD), with a width of 3 and a length of 4. I fold it diagonally so that vertex A touches vertex C. What is the length of the crease in the paper?

I have a drawing, containing all that I know so far (its not to scale). The red line is what I am supposed to find out. Also, I do not want to use any trigonometry functions, such as arctan, tan, sin etc.

Thanks.

I dont see how your going to get away without using trig functions

Ok, my class hasn't learned trig yet. But it looks like there is no other way.

I figured out how to prove that those two triangles are similar using trig...

Originally Posted by Grey

Ok, my class hasn't learned trig yet. But it looks like there is no other way.

I figured out how to prove that those two triangles are similar using trig...

ok, so now you have to just find the length of one of heights (using trig), multiply it by 2 and that's your answer

Originally Posted by Grey

I have a rectangular piece of paper (ABCD), with a width of 3 and a length of 4. I fold it diagonally so that vertex A touches vertex C. What is the length of the crease in the paper?...

Hello, Grey,

topsquark already has presented the complete solution:

1. map the triangle AFE to the triangle AF'E'. Then E'F' ║ DC.
2. You can use the proportion:

Code:

  x     3
---- = ---      solve for x
 2.5    4

     7.5     15
x = ----- = ----- = 1.875
      4       8

EB