Thursday, May 14, 2015

What is the largest number of sections of the rectangle?

In the rectangle at the right, line segment MN separates the rectangle into 2 sections. What is the largest number of sections into which the rectangle can be separated when 4 line segments are drawn through the rectangle?

When no lines are added, there is only one segment.
When one line is added, the number of segments is 2.
When two lines are added, the number of segments becomes 4.
When three lines are added, the number of segments becomes 7.

Observing the pattern, each time a line is added, that many segments gets added to the number of segments formed.

i.e; when three lines are added, it will be 4+3=7
So according to the pattern, when four lines are added, the number of segments = 7+4=11

Largest of number of sections into which the rectangle can be separated when 4 line segments are drawn is 11.
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6 comments :

  1. UnknownMay 9, 2019 at 5:58 PM

    11

    SOURCES:AOPS ALCUMUS

    ReplyDelete
  2. UnknownNovember 13, 2019 at 5:46 PM

    i thought it was 7

    ReplyDelete
  3. AnonymousOctober 8, 2020 at 8:57 PM

    They explained this answer so bad. EVEN A QUESTION WITH NO ANSWER WROTE BETTER THAN YOU!!!

    ReplyDelete
  4. UnknownOctober 27, 2020 at 6:57 PM

    Why don't you try to explain the question then and we'll see how you do

    ReplyDelete
  5. UnknownDecember 2, 2020 at 5:41 PM

    This makes the problem more confusing then it was

    ReplyDelete
  6. UnknownApril 27, 2021 at 4:33 PM

    ok this is bad cuz ma dad wil find out dat i looked at the internet cuz a 2nd grader aint dat smart

    ReplyDelete

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