The dimensions of a rectangle are 51 m and 49 m respectively while side of a square is 50 m. Which of the following statements is correct?

### Concept & Comparing Shapes When comparing a rectangle and a square, you must systematically evaluate their geometric properties: area, perimeter, and diagonals using standard formulas. $$ \text{Perimeter of Rectangle} = 2(l + b) $$ $$ \text{Perimeter of Square} = 4a $$ ### Step-by-Step Solution * Given: Rectangle dimensions $l = 51$ m, $b = 49$ m. Square side $a = 50$ m. * Check Area: Rectangle Area = $51 \times 49 = 2499\text{ m}^2$. Square Area = $50 \times 50 = 2500\text{ m}^2$. They are not equal. (Option d is incorrect). * Check Perimeter: Rectangle Perimeter = $2(51 + 49) = 2(100) = 200$ m. Square Perimeter = $4 \times 50 = 200$ m. They are equal! (Option c is correct). * Check Diagonals Equality: Rectangle Diagonal = $\sqrt{51^2 + 49^2} = \sqrt{2601 + 2401} = \sqrt{5002}$. Square Diagonal = $\sqrt{50^2 + 50^2} = \sqrt{5000}$. Not equal. (Option a is incorrect). * Check Diagonal Intersection: The diagonals of a square intersect at right angles, but the diagonals of a rectangle do not (unless it is a square). (Option b is incorrect). ### Exam Strategy & Shortcut Notice the numbers: 51, 49, and 50. The sum $51 + 49 = 100$, and $50 + 50 = 100$. Because their sums are equal, their perimeters will naturally be equal ($2 \times 100 = 200$). This immediately points to option (c). ### Common Pitfall Assuming that shapes with nearly identical dimensions will have equal areas. A square always has the maximum area for a given perimeter among all rectangles. ### Final Answer Therefore, the correct answer is **The perimeters of both the geometrical figures are equal.**.