Cut a rectangle in half

Geometry Level 4

Using a collapsible compass and a straightedge, how many moves are required to construct a line through a point A A that cuts a given rectangle into two parts of equal area?

Please refer to the terminology in this note for further definitions. See other problems in this set .

4 5 3 1 6 2

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

Sharky Kesa
Nov 27, 2016

Let the rectangle be P Q R S PQRS .

  1. Draw P R PR and Q S QS . Let them intersect at B B . (2 moves)

  2. Draw A B AB . (3 moves)

Here, we only require 3 moves.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

What did you mean by they share an angle A; could not get that part; though I solved the problem.

Yatin Khanna - 4 years, 6 months ago

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That was a bug reverting the problem to go back to a previous form of the question. Sorry.

Sharky Kesa - 4 years, 6 months ago

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Wow! That was fast, man! :) :P

Yatin Khanna - 4 years, 6 months ago

Did the same way.

Niranjan Khanderia - 4 years, 6 months ago

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