Square from a rectangle’s diagonal: A rectangle has length 3 cm and breadth 4 cm. A square has side equal to the rectangle’s diagonal. Find the area of this square (in sq. cm).

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:Rectangles with sides 3 and 4 form a classic 3–4–5 right triangle for the diagonal. The square built on that diagonal has side equal to the diagonal’s length. Given Data / Assumptions: Rectangle: L = 3 cm, B = 4 cm. Square side s = diagonal of rectangle. Concept / Approach:Diagonal d = √(L^2 + B^2). Area of square = s^2 = d^2. Step-by-Step Solution: d = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm.Square area = s^2 = 5^2 = 25 sq. cm. Verification / Alternative check: The Pythagorean triple (3, 4, 5) ensures no rounding. Square area equals diagonal squared, which is 25. Why Other Options Are Wrong: 16, 9, 4 correspond to squaring 4, 3, or 2 — not the diagonal length. Common Pitfalls: Mistaking the square’s side as one of the rectangle’s sides rather than the diagonal. Final Answer: 25 sq.cm

Square from a rectangle’s diagonal: A rectangle has length 3 cm and breadth 4 cm. A square has side equal to the rectangle’s diagonal. Find the area of this square (in sq. cm).

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