Question

On a board having 18 rows and 16 columns ,find the number
of rectangles ?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ On a board having 18 rows and 16 columns ,find the number}\hspace{.33em}\\~\\
& \normalsize \text{ of rectangles ?}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

23256

Answer 3

18C2*16C2 ?

Answer 4

theres a formula to find it :D
number of rectangles in an m x n grid can be given by -
\[\frac{ m(m+1)n(n+1) }{ 4 }\]

Answer 5

no i want methos i cant remeber formula

Answer 6

*method,*remember

Answer 7

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?

Answer 8

lol m confused

Answer 9

m+1C2*n+1c2

Answer 10

(Think of the dots formed at the corners of the little squares within the rectangle)

Answer 11

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)

Answer 12

m+1C2*n+1C2 is correct ?