What can be the lengths of two different sides of a rectangle whose area is 36 cm2?

univerkov | March 11, 2021 | education

As you know, the area (S) of a rectangle can be calculated by the formula S = a * b, where a and b are its sides.
Generally speaking, there are countless rectangles with an area of 36 cm2. If you need to find rectangles with an area of 36 cm2, provided that sides a and b are natural, then there are only 9. You can easily list them: 1 cm and 36 cm; 2 cm and 18 cm; 3 cm and 12 cm; 4 cm and 9 cm; 6 cm and 6 cm; 9 cm and 4 cm; 12 cm and 3 cm; 18 cm and 2 cm; 36 cm and 1 cm (note that the square is also a rectangle). If symmetric rectangles are counted as one rectangle, then rectangles with an area of 36 cm2, provided that sides a and b are natural, only 5.
Since, in the task, it is required to find rectangles with different (that is, not equal) sides, then we exclude a square with a side of 6 cm from the list.Thus, if the symmetrical ones are counted as one rectangle, then, provided that the sides are natural and unequal, rectangles with an area of 36 cm2 can have the following side lengths: 1 cm and 36 cm; 2 cm and 18 cm; 3 cm and 12 cm; 4 cm and 9 cm.

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