Question

The number of non-congruent rectangles that can be formed on a chessboard, is

• A. 30
• B. 32
• C. 33
• D. 36

Answer 1

The correct option is D 36

A chess board is in the shape of a square divided into $8\times 8$ smaller squares of equal dimensions.

If a rectangle formed has one side length $1$, then following (length, breadth) combinations possible:

$(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)$. Total $8$ non-congruent rectangles.

Similarly with one side as $2$ following non-congruent triangles possible:

$(2,2),(2,3),...,(2,8)$. Total $7$ non-congruent rectangles.

Similarly for $3,4,5,6,7,8$ we get $6,5,4,3,2,1$ non-congruent rectangles respectively.

So, total number of rectangles will be$=8+7+6+5+4+3+2+1=\frac{8\times 9}{2}=36$