Question

Consider a grid with $8$ parallel vertical edges and $9$ parallel horizontal edges, consecutive edges being separated by distance unity-
Find the number of rectangles in this grid which are not squares

• A. 1420
• B. 1220
• C. 1400
• D. 1320
• E. 1400

Answer 1

The correct option is A 1420

To find number of rectangle

number of rectangle $=m\frac{(m+1)}{2}\cdot n\frac{(n+1)}{2}$

$=9\times \frac{10}{2}\times 8\times \frac{9}{2}$

$=1620$

Number of square $=n\times m+(n-1)(m-1)+(n-2)(m-2)+(n-3)(m-3)$

$=9\times 8+8\times 7+7\times 6+6\times 5$

$=200$

Rectangles which are not squares$1620-200=1420$

Answer