Question

Find the number of rectangles in the adjoining figure(a square is also considered a rectangle):







Find the number of rectangles in the adjoining figure(a square is also considered a rectangle):

Answer 1

figure is in attachments

Answer 2

anyone please !!! help me

Answer 3

You are right..its 6*12

Answer 4

no its answer is not 6*12
as you can see there 2square also make a rectangle so we have to calculate allof them

Answer 5

So, its a bit logical kind..okay, I'll check it

Answer 6

6*12 means there are 6 row and 12 column

Answer 7

Its 12! x 6!

Answer 8

i can give you a way ...becoz i solved a question in which there was a rect with 4*4 dimention ..so i solved it by
no of 4*4 square=1
no of 3*3 square=4 we can write it 2^2
no of 2*2 square=9 ........3^2
no of 1*1 square= 16 .....4^2
it become a series
1^2+2^2+3^2+4^2
and solved it by formula n(2n+1)(n+1)/6

Answer 9

opctions are a..864 b.3276 c. 1638 d.. None of these

Answer 10

The answer I got was too large in number..Just a sec

Answer 11

i got it how to solve
first no of rectangle =6*12
then 6*(12-1)
similarly 6*(12-2) ,6*(12-3),6*(12-4) ........6*(12-1)
is that right

Answer 12

No no that's cant be right...It gives the number of boxes and you are repeating many of them

Answer 13

take an example of 2*6 rectangle and calculate no of boxes

Answer 14

Calculate the answer you got...

Answer 15

468 but now i think its was some how not correct

Answer 16

i take rectangle of 1*1,1*2,1*3,1*2
but not take 2*3,2*4.....we will have to take this too

Answer 17

Its not 12! x 6!..its a typo sorry..its \[\sum_{1}^{12}n \times \sum_{1}^{6}n = 1638\]

Answer 18

wts the logic u apply here

Answer 19

Take one row at first...how many rectangles can you select? 12boxes at a time in 1 way, 11boxes at a time in 2 ways, 10boxes at a time in 3 ways......1box at a time in 12 ways..So, the sum is sigma12..there are six such rows..so, sigma12 x 6 ways...now, select two rows at a time and you can do that in 5 ways..the total no. of rectangles are sigma12 x 5...now three rows and you get sigma12 x 4...Likewise, the total number of rectangles are :
sigma12(6+5+4+3+2+1) = sigma12 x sigma6 = 1638

Answer 20

Try it and tell me when you understand it...

Answer 21

confused but trying