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Square from a rectangle’s diagonal:\nA 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).

Difficulty: Easy

Correct Answer: 25 sq.cm

Explanation:


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
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