The perimeter of a rectangle is 30 cm. The length and breadth of the rectangle are integers in cm. Find the number of possible pairs of length and breadth in cm.

The correct answer is: Total 7 pairs of length & breadth in cm are possible.

Hint:-
Perimeter of a rectangle = 2 (length + breadth)
Step-by-step solution:-
We know that Perimeter of a rectangle = 2 (length + breadth)
∴ Perimeter of the given rectangle = 2 (length + breadth)
∴ 30 = 2 (length + breadth)
∴ 30 / 2 = length + breadth
∴ 15 = length + breadth
i.e. length + breadth = 15 cm ..................................... (Equation i)
We need to find all the possible combination of lengths & breadths that would add up to 15 i.e. satisfy Equation i.
∴ The possible combinations are-
(Length, breadth) = (14,1); (13,2); (12,3); (11,4); (10,5); (9,6); (8,7)
∴ Total 7 pairs of length & breadth in cm are possible.
Final Answer:-
∴ Total 7 pairs of length & breadth in cm are possible.
Note:-
Theoretically, (1,14); (2,13); (3,12); (4,11); (5,10); (6,9); (7,8) also add up to 15 but for a rectangle, length should always be greater than breadth.
∴ these combinations are not possible for the given question.