Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.\nGive the answer in sq cm.

Introduction:
This question tests the use of Pythagoras theorem to find the diagonal of a rectangle and then using that diagonal as the side of a square. The diagonal of a rectangle forms the hypotenuse of a right triangle whose legs are the rectangle’s length and breadth. Once the diagonal is found, the square’s side is known directly, and the area is the square of that side. This is a short and direct question, but it checks whether you correctly identify the diagonal formula and avoid confusing diagonal with perimeter or area.

Given Data / Assumptions:

• Rectangle length = 3 cm
• Rectangle breadth = 4 cm
• Rectangle diagonal d = sqrt(L^2 + B^2)
• Square side = d
• Square area = side^2

Concept / Approach:
Use Pythagoras theorem: d = sqrt(3^2 + 4^2). Then square area = d^2. Notably, area becomes (3^2 + 4^2) directly because (sqrt(x))^2 = x. This gives a very clean computation.

Step-by-Step Solution:
Diagonal d = sqrt(3^2 + 4^2)d = sqrt(9 + 16) = sqrt(25) = 5 cmSquare side = 5 cmSquare area = 5^2 = 25 sq cm

Verification / Alternative Check:
The 3-4-5 right triangle is a standard Pythagoras triple, so the diagonal being 5 cm is immediately consistent. If the square side is 5 cm, its area must be 25 sq cm. Also note the shortcut: square area = d^2 = (3^2 + 4^2) = 25 directly, confirming the same result without computing the square root explicitly.

Why Other Options Are Wrong:
16 or 9: correspond to using 4 or 3 as the square side (ignoring diagonal).4: usually comes from confusing breadth with diagonal.20: comes from using 3*4+? or misapplying formula.

Common Pitfalls:
Adding 3 and 4 to get diagonal (incorrect; diagonal uses squares).Using rectangle area (12) as diagonal or square side (nonsense).Forgetting the square side equals diagonal, not half diagonal.Arithmetic error in 3^2 + 4^2.

Final Answer:
25 sq cm