A rectangle of perimeter 276 cm is cut into five equal squares. Find the area of each square.

The correct answer is: Area of each square is 529 cm2.

Hint:-
i. Area of a square = side2
ii. Perimeter of a rectangle = 2 (length + breadth)
Step-by-step solution:-
In the adjacent diagram, let the side of each square be x cm
∴ length of the entire rectangle = 5 × side of each square
∴ length of the entire rectangle = 5 × x = 5x ............................................ (Equation i)
Also, breadth of the rectangle = side of 1 square = x ............................... (Equation ii)
Now, Perimeter of a rectangle = 2 (length + breadth)
∴ Perimeter of the given rectangle = 2 (length + breadth)
∴ 276 = 2 (5x + x) ....................................... (From Equations i & ii)
∴ 276 = 2 (6x)
∴ 276 = 12x
∴ 276 / 12 = x
∴ 23 = x
i.e. Side of each square = x = 23 cm ..................................... (Equation iii)
Now, we know that area of a square = side2
∴ Perimeter of the given square = x2
∴ Perimeter of the given square = 232 ........................................... (From Equation iii)
∴ Perimeter of the given square = 529 cm2
Final Answer:-
∴ Area of each square is 529 cm2.