Q.

How many rectangles are there in the following figure?

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a

48

b

60

c

61

d

56

answer is B.

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Detailed Solution

No. of Rectangles

1 Unit:- Total 12

2 Unit:- 

(1,2)  (2,3)  (1,4)  (2,5)  (3,6)  (4,5)  (5,6)(4,7)  (5,8)  (6,9)  (7,8)  (8,9)  (7,10)(8,11)(9,12)(10,11)(11,12)17

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3 Unit:- (1,2,3)  (4,5,6)  (7,8,9)  (10,11,12)  (1,4,7)

(4,7,10)  (2,5,8)  (5,8,11)  (3,6,9)  (6,9,12)

4 Unit:- (1,4,7,10)  (2,5,8,11)  (3,6,9,12)  (1,2,4,5)

(2,3,5,6)  (4,7,5,8)  (5,6,8,9)  (7,10,8,11)  (8,9,11,12)9

6 Unit:- (1,2,3,4,5,6)  (4,5,6,7,8,9)  (7,8,9,10,11,12)

(1,4,7,2,5,8)  (2,3,5,6,8,9)  (4,5,7,8,10,11)  (5,6,8,9,11,12)78 Unit:- (1,2,4,5,7,8,10,11)  (2,3,5,8,9,11,12)​ 2

9 Unit:- (1,2,3,4,5,6,7,8,9)  (4,5,6,7,8,9,10,11,12)2

Whole Rectangle1

Total=12+17+10+9+7+2+2+1=60

Method – 2

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(1+2+3)×(1+2+3+4)

60

 

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