Jump to content
BrainDen.com - Brain Teasers
  • 0
BMAD

Area of an infinitely shaded region

Question

Suppose you have a triangle that has 2-1 inch lengths. Divide this triangle into half by drawing a line from vertex between the two identical sides,  choose one of the sides randomly and shade it.  The non-shaded side is cut in half again.  Choose one of these sides randomly and cut it in half again shading one random piece.  If this pattern of cut, shade, cut, cut, shade, cut, cut, shade cut, cut,.... was to be continued forever, what would be the area of the shaded region?

Share this post


Link to post
Share on other sites

5 answers to this question

Recommended Posts

  • 0
Spoiler

... if it is a right triangle. In other instances the shaded area would equal the area of the original triangle.

 

Please ignore my answers above - wrong, since there are two cuts in between!

Spoiler

 

 

Share this post


Link to post
Share on other sites
  • 0
On 11/12/2018 at 9:12 AM, Donald Cartmill said:

The area would be that of the original triangle,however that area would vary as determined by the length of the 3rd side  

I agree that it will vary but we can bound the area. 

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...

  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...