Consider a 6×6 square which is dissected into 9 rectangles by lines parallel to its sides such that all the rectangles have integer sides. Out of 9 rectangles what is the maximum number of congruent rectangle

(Q). Consider a 6×6 square which is dissected into 9 rectangles by lines parallel to its sides such that all the rectangles have integer sides. Out of 9 rectangles what is the maximum number of congruent rectangle ?
Solution:-

Let us solve this problem diagramatically:-

Since we are to dissect 6×6 square with 9 rectangles so make the 9 rectangles starting with least possible areas:-
1 ⟹ 1×1
2 ⟹ 1×2
3 ⟹ 1×3
4 ⟹ 1×4 or 2×2
5 ⟹ 1×5
6 ⟹ 1×6 or 2×3
8 ⟹ 2×4
When we make diagram of these rectangle then we see that we are bond to get 2 congruent rectangles for 1×5 & 2×4.
So we will get 2 congruent Rectangles        Answer