BECE Mathematics 2020 Paper

Concept:When two shapes have the same perimeter, equate their perimeters and then find the required area.Solution:Perimeter of a rectangle $= 2(\text{length} + \text{breadth})$.Given length $= 10 \text{ cm}$ and breadth $= 6 \text{ cm}$.So, perimeter of the rectangle $= 2(10 + 6) = 2 \times 16 = 32 \text{ cm}$.The square has the same perimeter, so its perimeter is also $32 \text{ cm}$.Let the side of the square be $s$.Perimeter of a square $= 4s$.Thus, $4s = 32$.Dividing both sides by $4$: $s = \frac{32}{4} = 8 \text{ cm}$.Area of the square $= s^2 = 8^2 = 64 \text{ cm}^2$.Answer:Option D ($64 \text{ cm}^2$)