Question

The number of triangles with vertices belonging to normal 8x8 chess board is
1) 2112 2) 2148 3) 2136 4) 2116
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Answer 1

Explanation:

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

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

. Total non-congruent rectangles.

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

. Total non-congruent rectangles.

Similarly for we get non-congruent rectangles respectively.

So, total number of rectangles will be