Division and Distribution into Groups of Equal Sizes
A rectangle w...
Question
A rectangle with side lengths as 2m−1 and 2n−1 units is divided into squares of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is
A
(m+n−1)2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4m+n−1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
m2n2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
m(m+1)n(n+1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Cm2n2 Along horizontal side one unit can be taken in =(2m−1) ways 3 units can be taken in =(2m−3) ways 5 units can be taken in =(2m−5) ways and so on
∴ The number of ways of selecting a side horizontally is (2m−1)+(2m−3)+(2m−5)+...+3+1=m2
Similarly the number of ways of selecting a side vertically is (2n−1)+(2n−3)+(2n−5)+...+3+1=n2 ∴ total number of rectangles = m2n2