Max@Math Revolution wrote:How many rectangles can be formed by connecting the grid points from the figure above? (Diagonal connection of grid points is not permitted)
A. 72
B. 96
C. 108
D. 192
E. 315
To form a rectangle, we must combine a HORIZONTAL LENGTH with a VERTICAL LENGTH:
Horizontal length:
Number of ways to choose a horizontal length of 1:
AB, BC, CD, DE, EF, FG = 6
Number of ways to choose a horizontal length of 2:
AC, BD, CE, DF, EG = 5
Number of ways to choose a horizontal length of 3:
AC, BE, CF, DG = 4
Number of ways to choose a horizontal length of 4:
AD, BF, CG = 3
Number of ways to choose a horizontal length of 5:
AF, BG = 2
Number of ways to choose a horizontal length of 6:
AG = 1
Total ways = 6+5+4+3+2+1 = 21
Vertical length:
Number of ways to choose a vertical length of 1:
AH, HI, IJ, JK, KL = 5
Number of ways to choose a vertical length of 2:
AI, HJ, IK, JL = 4
Number of ways to choose a vertical length of 3:
AJ, HK, IL = 3
Number of ways to choose a vertical length of 4:
AK, HL = 2
Number of ways to choose a vertical length of 5:
AL = 1
Total ways = 5+4+3+2+1 = 15
To combine our horizontal options with our vertical options, we multiply:
21*15 = 315
The correct answer is
E.
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