There is a rectangle sheet of dimension (2m - 1) x (2n - 1), (where m > 0, n > 0). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length.
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Answer:
Correct option is D)
Total no. of horizontal line=2m
Total no. of vertical lines=2n
(∵ Each line is at unit distance and hence, total no. of lines=Distance/lenght +1).
To form a square from three lines,we must select one even and one odd numbered horizontal and vertical line.
∴ Ways possible of selecting such squares=(C
1
m
×C
1
m
)×(C
1
n
×C
1
n
)
=C
1
m
×C
1
m
×C
1
n
×C
1
n
=m
2
×n
2
=m
2
n
2
Answer:
Total no. of horizontal line=2m
Total no. of vertical lines=2n
(∵ Each line is at unit distance and hence, total no. of lines=Distance/lenght +1).
To form a square from three lines,we must select one even and one odd numbered horizontal and vertical line.
∴ Ways possible of selecting such squares=(C
= m^2n^2