BrainDen.com - Brain Teasers
• 0

# Cutting a cut Square

## Question

You have a square with an area of 1 m2. You cut the square along its diagonal. Working with half of the square, you cut the square again but this time you cut a straight line that halves the half shape without bisecting the (remaining 90 degree) angle. The result of the cut leaves a triangle and a quadrilateral. Find the length and location of the shortest straight cut which divides the board into these two parts of equal area.

## Recommended Posts

• 0

The minimum length cut makes an isosceles triangle with a 45 degree corner as the apex.

To make a triangle with area 1/4, the cut should be made between two points each .8409 m from the apex.

The length of that cut will be sqrt [ tan (pi/8) ] = .6436 m long.

## Join the conversation

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

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

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