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OpenStudy (anonymous):
@ganeshie8
OpenStudy (mathmath333):
|dw:1440718821577:dw|
OpenStudy (mathmath333):
\(\large \color{black}{\begin{align}
& \normalsize \text{Find the number of rectangles.}\hspace{.33em}\\~\\
\end{align}}\)
OpenStudy (mathmath333):
the lines are perpendicular to each other.
OpenStudy (chillout):
Begin by choosing two pairs of horizontal lines and two pairs of vertical lines so you can have a rectangle.
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OpenStudy (anonymous):
I just know theres a ton
OpenStudy (chillout):
Let \(\left(\begin{matrix}a \\ 2\end{matrix}\right)\) be the number of vertical lines that can be picked, and \(\left(\begin{matrix}b \\ 2\end{matrix}\right)\) the number of horizontal lines that can be picked. For each pair of horizontal lines, there's a pair of vertical lines that will form a rectangle with them.
Therefore you have \(\left(\begin{matrix}n \\ 2\end{matrix}\right)\)*\(\left(\begin{matrix}b \\ 2\end{matrix}\right)\) as the number of rectangles.
OpenStudy (chillout):
That would be my guess :)
OpenStudy (mathmath333):
n=4,b=6 ?
OpenStudy (chillout):
Yes. And sorry, meant to be "a" in the last line.
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