mathmath333
  • mathmath333
On a board having 18 rows and 16 columns ,find the number of rectangles ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ On a board having 18 rows and 16 columns ,find the number}\hspace{.33em}\\~\\ & \normalsize \text{ of rectangles ?}\hspace{.33em}\\~\\ \end{align}}\)
imqwerty
  • imqwerty
23256
mathmath333
  • mathmath333
18C2*16C2 ?

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imqwerty
  • imqwerty
theres a formula to find it :D number of rectangles in an m x n grid can be given by - \[\frac{ m(m+1)n(n+1) }{ 4 }\]
mathmath333
  • mathmath333
no i want methos i cant remeber formula
mathmath333
  • mathmath333
*method,*remember
imqwerty
  • imqwerty
ok then try finding out the solution this way- How many ways can I draw two horizontal lines and two vertical lines through an array of (m+1) by (n+1) dots?
mathmath333
  • mathmath333
lol m confused
mathmath333
  • mathmath333
m+1C2*n+1c2
imqwerty
  • imqwerty
(Think of the dots formed at the corners of the little squares within the rectangle)
imqwerty
  • imqwerty
The two horizontal lines can be drawn C(m+1,2) ways, and the two vertical lines can be drawn C(n+1,2) ways, so the total number of rectangles within an m x n rectangle isC(m+1,2) C(n+1,2)
mathmath333
  • mathmath333
m+1C2*n+1C2 is correct ?

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