Question

Below is a square grid of 8$\times$8


How many rectangles of different dimensions in a grid.

• A. 34
• B. 35
• C. 36
• D. 33

Answer 1

The correct option is C 36

Rectangles of

$1\times 1,1\times 2,1\times 3,1\times 4,1\times 5,1\times 6$
$1\times 8\Rightarrow rectangles$

$2\times 2,2\times 3,2\times 4,2\times 5,2\times 6,2\times 2$

$\Rightarrow 7rectangles$

$3\times 3,3\times 4,.........3\times 8\Rightarrow 6rectangles$
$4\times \mathrm{4........4}\times 8\Rightarrow 5rectangles$
$5\times 5.........5\times 8\Rightarrow 4rectangle.$

$6\times 6,6\times 7,6\times 8\Rightarrow 3rectangles$
$7\times 7,7\times 8\Rightarrow 2rectangles$
$8\times 8=1rectangles$

Hence total no. of rectangles
= 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= 36 rectangles